Quay Park is the area around whatever they call Vector Arena these days. It's on the periphery of the city centre atm but is a much better location than Eden Park because it's just a short flat walk to down Quay Street to Britomart (the main train station whose capacity is about to explode when the City Rail Link is complete) and the rest of downtown. The Britomart end of Quay Street - and Britomart in general - already has plenty of bars and eateries around and Commercial Bay (latest fancy shopping + dining destination) is across the square from the train station.
Eden Park, on the other hand, were diabolical to get to and from, and is surrounded by absolute wounder residents who seem to think the entire city should shutdown at 6PM because that's when they doze off to sleep. The only thing Eden Park has going for it is history and that's not enough against the actual benefits of a central city destination stadium.
The waterfront ones, especially the sunken one, were both daft.
tldr: build city centre stadium because it has better transit connections, surrounding hospitality, and isn't trying to be both a cricket and rugby stadium.