Taxis in Queenstown are common, and make it very easy to get around. They're obviously more expensive than the Connectabus, but if you're only using them for a quick ride somewhere, they won't break the bank.
Queenstown Taxis are all privately run and are easy to find at the aiport and in the CBD. Most journeys have fixed rates, so do ask when you get in, to avoid any nasty surprises on the meter. For larger groups minibus shuttles go anywhere you like - airport, golf courses, attractions, even restaurants.