One of them is Mount Meru, which stands in the little-visited Arusha National Park and which I had come here to scale.
Arusha can't compete with the Serengeti on size or diversity but it is spectacularly pretty, with lakes and forests and its own mini Ngorongoro crater.
There are no lion or cheetah, but there are hyena, leopard and elephant.
There has been an eight-year drought in the region, but when we visited recently the rains had finally come and the bush was lush once more.
We saw buffalo, troops of baboons, wallowing warthogs and docile waterbuck.
We spotted tiny, twiggy-legged impala and stocky, robust little zebras, perfect miniatures of the adults.
Bushes and trees were all sprouting, and in a forest of acacias we discovered more than 30 giraffe delicately plucking the new shoots from among the thorns with their long, black tongues.
Bird watching
My very first trip to Africa, 20 years ago, got me excited about birds.
The first glimpse of a lilac-breasted roller - common as muck all over sub-Saharan Africa - and wham! You're hooked.
It's not just the evocative name, it's the vibrancy of its plumage and the fact that it perches for an obligingly long time on the end of branches, or on telegraph wires, making it easy to spot, watch and photograph.
Then there are the bee-eaters, the kingfishers (far less elusive than our own), the pale chanting goshawks - all spectacular, and all easy to identify.
My husband Ludo and I met up with our guide, Mark Baker, whose prodigious knowledge was inherited from his parents, who have spent the past quarter-century travelling the length and breadth of Tanzania collecting data for the most comprehensive encyclopaedia of birds ever attempted.
The beauty of birding with someone on their "patch" is that we saw things we would never otherwise have spotted.
Olive white-eyes hopped about, almost perfectly camouflaged in the branches of a fig tree; darting, iridescent sunbirds; a paradise flycatcher - the male, with his orange streamer of a tail - and what Mark described as a "good bird", an Abyssinian thrush, is rarely seen, yet was pecking for insects just a few metres away from us.
In a thickly wooded area, we sat just watching and listening.
A streak of red flashed across the track in front of us and was gone.
"Narina Trogon!" exclaimed Mark.
"You often see them here but if they don't fly, it's almost impossible to spot them."
The startling red is revealed only in flight, otherwise the bird, which tucks itself away high in the tree canopy, merges with the leaves. We searched, scanning the branches.
Through my binoculars I picked up something black and white with fur, rather than feathers: Colobus monkeys, a pair, grooming and unaware they were being watched.
A bank of cloud was bubbling up on the horizon, promising rain.
First sight
Mark dropped us off at one of the park's so-called "special campsites" where we were greeted by Bonaventure (a guide), Menase (a cook), mugs of tea and one of the most beautiful spots to pitch a tent I've ever seen.
"There's your mountain," said Bonaventure.
Looming above us was the craggy outline of Mount Meru.
At 4566m, it ranks as the fifth-highest mountain in Africa, but is climbed by only a few hundred, rather than a few thousand, people a year.
Like Kilimanjaro, it is an extinct volcano.
The last time it erupted the explosion tore a great chunk out of the side of the crater, leaving what had been described to me as a "knife-edged ridge" to the summit.
As someone who has a healthy fear of falling off things, the knife-edged ridge looked impossibly foreboding from where we were standing.
But before I could get cold feet, rain clouds hid the mountain and Menase announced the chicken was cooked.
"Eat! Eat! Eat!" he urged.
"You need plenty of energy for tomorrow." So we feasted and retired to our tent as the rain fell and a hyena's whooping call reverberated through the trees.
"That's quite a big herd of buffalo," said Ludo, "and it looks like we're going to have to walk straight through it."
We watched as Menase, who had set off with the porters ahead of us, stopped at the edge of the herd, clapped his hands and shouted.
Buffalo are belligerent creatures at the best of times and can be downright dangerous.
This lot regarded Menase with the sort of expression perfected by Catherine Tate, before deciding to move, oh so slowly, just off the path.
I saw Mechama, a park ranger, tighten his grip on his gun.
We saw a lot of wildlife, thanks largely to the fact that Mechama, in front, walked with exaggerated slowness as if he was playing grandmother's footsteps.
As someone who tends to charge up hills, this was infuriating.
"Deal with it," said Ludo, "he's got the gun and we need to stay together. If you go racing off you might get eaten."
I plodded on, sulking, until the peace was shattered by a strangled squawking. Hornbills.
We stopped to look at them and at the same time noticed a giraffe and then a herd of zebra.
Swallowtail butterflies flitted past us and crickets scattered beneath our boots.
We crossed grassy plains, boulder-hopped over rivers and walked through a forest of ancient mossy trees following the tracks of a leopard imprinted in the mud.
And the climb of 1,250m from the park gate to the first camp at Miriakamba felt VC effortless.
Camp two
Arriving blister-free and perky, we settled down on the grass outside the huts in the sun, watching the white-necked ravens and both silently thinking that this climb was going to be a breeze - until a group arrived from the opposite direction.
Mount Meru is climbed in three or four days.
The first night is spent at Miriakamba, the second at the Saddle.
The walk to the summit begins at around 2am on the third morning, and climbers will then either descend to Miriakamba that same day or push on, as we intended to do, and reach the park gates at the end of the third day.
The 10 bedraggled, mud-spattered people who came straggling into camp scattering walking poles and sodden ponchos had attempted the summit that morning.
"Bloody hell, they look half-dead," Ludo observed.
"It was tough," one of them admitted later, fortified by hot food and cold beer.
We were standing outside the dining hut.
The cloud, which had shrouded the peak all day, had cleared and it stood out, a hard, black outline against the night sky.
"It was very cold and very windy.
It took over six hours to get to the summit and the climb was much harder than I imagined."I was about to ask him about the ridge, but I had heard enough already to render me sleepless.
"You awake?" I whispered to Ludo from my bunk.
"Yes," came the muffled reply from the depths of his sleeping bag.
"That guy was Austrian. He spends his life climbing mountains. And he had all that kit - gloves, waterproof everything, poles. And he still found it really tough and really cold. We're going to die up there."
We had what we thought we'd need to climb a not-particularly-high mountain - good boots, gaiters, a warm layer and a waterproof coat.
It appeared we were seriously under-equipped.
Unbeknownst to us, Bonaventure was on the case.
A hugely experienced mountain guide, he'd kept a careful eye on us, constantly urging us to drink plenty of water - "Your pee must be clear and copious!" - and to eat enough.
The following morning he joined us for Menase's hearty mountain-climbers' breakfast - porridge, eggs, bacon, toast, cake - with a bundle under his arm.
He unravelled two pairs of waterproof trousers - Menase's own pair for Ludo and a voluminous, startlingly turquoise pair for me, loaned by the camp supervisor for $5.
They would make all the difference and Bonaventure's thoughtfulness couldn't have been better timed.
Moments later, thunder heralded blinding sheets of rain.
We sat it out until it eased to a drizzle and then began to climb - slowly, slowly, up steep wooden steps built against the sheer muddy side of the mountain.
The forest we were walking through was full of flowers, butterflies and buzzing beetles.
When the steps ran out the going got harder, the wet mud sticky and slippery, but at Mechama's steady 2km per hour we made good progress and before long we noticed that the vegetation had completely changed.
We'd left the trees behind and were walking through giant heathers and clumps of yellow-flowered St John's wort.
A series of switchbacks gave us our first glimpse of the camp perched on a saddle between the peaks of Mount Meru and Little Meru.
As soon as we stopped walking we realised how much colder it was here, 1,000m above the last camp.
We sat huddled in the communal area of the sleeping hut surrounded by dripping gloves, hats and raincoats.
The front step was crowded with abandoned pairs of sodden boots and around the tables sat a glum crowd, hunched against the cold.
Finally I plucked up the courage to ask whether they had made it to the summit that morning.
"We had rain, then sleet, then hail, then snow," shivered a German woman. "I have never been so wet and so cold."
Bonaventure had told us as we walked up Little Meru, a gentle hour's plod above camp, that only five of a group of 14 had made it to the summit that morning.
The summit of Little Meru was shrouded in thick cloud when we reached the cairn at 3,801m.
The peak of Meru was totally obscured.
We started back down, only to round a bend and see that the clouds had parted - and there was Kilimanjaro, in all her snowy glory, standing like a giant baked Alaska in a sea of cloud.
"And look at that!" cried Bonaventure, and we turned 180 degrees to see the whole of Meru revealed and, just visible, the flag that marks the summit.
It looked very, very far away. I was too nervous to sleep. To get to the summit, all we had to do was gain 800m in altitude. And not fall off the knife-edged ridge.
The ascent
At 1am, as we were struggling into our boots, I considered bowing out, but Menase, who wasn't even coming to the summit with us, had got up to make us good-luck porridge.
Our little band set off an hour later, Mechama in front, Bonaventure at the back, Ludo and I between them, walking in the beam of our head torches.
The air was absolutely still and it was dry.
"Don't think about the ridge, don't think about the ridge," I muttered in time with my steps.
I looked up to the round-shouldered mass of Rhino Point above us and saw a pin-prick of light.
I assumed it was the head torch of one of the group that had set off earlier, but then I looked again.
"It's a star!" The sky was clearing. We could see lights in the valley and above us more and more stars started to appear.
We were walking on what appeared to be a ridge of black volcanic sand, but it was wide, flat and easy to walk on.
"This is fine," I thought, "not knife-edged at all."
All my fears dissipated and I realised I was grinning. Not for long.
The path ended and was replaced by a rock face, along which we had to inch on tiny footholds with what appeared, in the dark, to be a bottomless drop below us.
I froze, palms sweating, breathing hard.
"I can't do this." Mechama was getting further ahead.
I couldn't move.
Then a warm hand grasped mine and Bonaventure stood between me and the gaping abyss.
"Don't hold the rock, hold me," he said and marched me firmly across before I could utter a squeak of protest.
Wobbly with relief, we began a long, steep climb through sand and then a scramble between pillars and pinnacles of lava.
Suddenly I realised I was going to be all right.
Black against the dark sky, craggy peaks rose above us.
We walked beneath an overhang, along a ledge.
Light began to take the edge off the darkness and below us we could make out wonderfully chaotic lava sculptures, a jumble of crags and spikes and boulders.
Another calf-burning sand slope and it felt like we were getting close.
Ludo leant against a rock.
He looked dreadful - ashen and sickly.
"Just need to rest a bit," he croaked.
It was the altitude.
Bonaventure persuaded him to drink some water, even though he didn't want it, and after a few minutes we were able to go on.
Stopping and starting we inched our way upwards, Bonaventure watching Ludo all the time.
Suddenly, I spotted the flag that marks the summit; pain and exhaustion were forgotten instantly, and euphoria took over.
A final scramble and we'd made it.
The sun had come up, the cloud had followed it, we were surrounded by thick, ghostly mist and couldn't see a thing.
But it didn't matter.
We'd done it.
Now all we had to do was get down.
- INDEPENDENT
