In Grey Lynn/Westmere the rental cost of a three-bedroom home has fallen from $503 a week to $494 - a decrease of 4 per cent.
Remuera has seen a drop of 6 per cent with rents falling from an average of $661 to $620.
Property commentator Alistair Helm said three-bedroom rental homes in and around the central city were becoming less common because the yields on these properties were so low.
Mr Helm said the issue seemed to be one of a lack of supply driven by a buoyant selling market in which vendors were trying to cash in.
He was at an auction for a villa in Grey Lynn yesterday where a house in Rose Rd sold for $2.4million.
"When you are pushing that kind of price there is no way you could make any money renting that ... you would need about $2000 a week and no one is going to pay that, so why would you enter the rental market in these areas?
"It's better to sell off rentals, do them up and flog them off for a couple of million.
"There's so much renovation going on in Grey Lynn, Ponsonby and those kinds of areas and we are not talking about a bit of tarting up but we are talking half a million-plus in renovation costs."
Mary Taylor, property manager for Ray White's Parnell rental office, said longer-term tenancies in popular central Auckland suburbs could also be a factor.
"People are well aware that the central city properties are harder to get at the beginning of the year. I don't think we had as much movement, that's probably a factor."
Over the bridge, Devonport and Takapuna/Milford have seen 8 per cent and 11 per cent increases respectively for the cost of renting a three-bedroom home.
Lower-cost rental options are found in the Pukekohe/Tuakau/Waiuku, Papakura, Manukau/Manurewa, and Mangere/Otahuhu/Otara areas with rents remaining below $460 - although most of these places saw an average increase of about 4 per cent for the period.
Papakura saw a 29 per cent increase for the cost of renting a one-bedroom flat or unit with the average rent going up from $205 a week to $264.
Going down (for a three-bedroom home)
$503 a week to $494 for Grey Lynn/Westmere
$661 to $620 for Remuera