Not missing anything. Central city hotels are far nicer than the airport based ones, and generally comparable cost. There are plenty of good central hotels - no need to stick with Hyatt particularly, although there aren't too many US chain hotels in NZ.

At that time of day the cab ride to the airport is quick (only a few minutes longer than getting a shuttle from airport hotel by time factor in wait), or you could even take the airbus from Queen St if you have carry on only (nearest airbus stop is a couple of blocks down the hill from Hyatt).