I can absolutely recommend the apartment!
I stayed for 12 days and did Queenstown&surrounding without a car.
What I absolutely loved was: the apartment itself (quiet and beautifully furnished, dishwasher&washing machine very helpful), the hot spa, the close supermarket, the bee card (for public transport essential), the only 10 min walk to the center ...
I can further absolutely recommend: the Park Run (every Saturday at 8 am in Queenstown Gardens), Ben Lomond Summit (I started off from the apartment 1 hour before sunrise; took me 3 hours from apartment through Tiki Trail to summit - was terrific), the Kiwi Birdlife Park (ticket allows you to go there for 3 consecutive days), swimming in the Lake Hayes, walking the Lakeside Trail mostly by the waterfront on the stony beach, morning jogging to the Sunshine Bay... well, there is a lot more, also don't miss the wetlands just behind the apartment (Matakauri Park) - you find e.g. wild oregano.