He wants it to receive a major upgrade to bring it into line with international standards and said he would work to transform the stadium into a multi-sport, multi-event centre, hosting up to six major non-sporting events a year.
Eden Park is owned by the Eden Park Trust, not by council. Concerts have to overcome legal hurdles regarding noise control.
Tamihere's strategy included exploring developing a self-funding covered multi-sport venue on the number two ground.
"We can't have Aucklanders being held to ransom by a few neighbourhood nimbys, nor can we fund stadia for every code."
Auckland Council last month approved a $63-million package - including a no-strings grant of $10 million - that is expected to secure Eden Park's future for the next 10 to 15 years.
That leaves open the possibility that it could eventually be replaced by a stadium built on the waterfront or elsewhere.
Last month the council extended Speedway's lease at Western Springs for another 12 months after the parties failed to agree on an alternative venue.
Tamihere has also committed to retaining Chamberlain Park public golf course in its current 18-hole format.
In response to population growth requiring more facilities, the council was planning to reduce it to nine holes and use the available area for other recreational purposes.
Under the plan, which is currently on hold, it wants to carve a 3.3ha park out of the golf course, which would include a driving range, two multi-use sports fields, a public park and a pedestrian and cycle path through the eastern edge of the site.
There was also the possibility the Mt Albert Aquatic Centre (currently next to Mt Albert Grammar School) would be rebuilt at the park.
Tamihere wants major sports bodies to work together as the country can no longer afford the one sport per stadium concept.
"They will have to identify how they fit into the current stadia facilities, and in some cases cohabit and cooperate with other sports."
An alternative location would be identified and developed as a high-performance facility for Auckland Cricket and New Zealand Cricket and for tests.
Short-form cricket - ODIs and T20 games - would remain at Eden Park.
Tamihere, whose running mate is Christine Fletcher, said he would support investigations into more effective use of the Domain, Auckland's most iconic park.
He pledged more money for Regional Parks and improvements to facilities such as walking tracks, toilets and information centres and creating a "People's Precinct" integrating - and in some cases linking with 'green bridges' - Western Springs Park, Chamberlain Park, Jaggers Bush Reserve, Meola Reef Reserve, the Zoo and MOTAT.
Tamihere said these strategies would be funded from rates, central government and the open space development contributions levied on all new dwellings and developments.
"We need to start regarding our recreational facilities as being as important as other infrastructure, such as roads and sewers.
"Do we want a city where our kids have nowhere to play … premier events are staged at venues which we frankly should be ashamed of?"