There are an awful lot of beautiful places in New Zealand. In my travels, the place that really captured my heart the most in terms of beauty was Wanaka, which isn’t far from Queenstown.
It’s a small town on Lake Wanaka which has plenty of charm. In town itself there aren’t a huge amount of activities, but sitting by the lake is a great activity in itself.
Not far from town, there are lots of hikes and the fun-even-for-adults Puzzling World.
Of course, this is New Zealand, so there are lots of adventure activities that can be booked from town (most offer pickup from town), so whether you want to go skydiving, take a scenic flight, paragliding, bungee jumping, jet boating, rock climbing, canyoning, mountain biking, horseback riding, etc, you can do it here.
My first time in Wanaka, my camera ceased functioning so I bought a disposable one. On that trip I did horseback riding and went to Puzzling World, as well as a nice day hike.
Somewhat strangely, Backcountry Saddle Expeditions has only Appaloosa horses (a Native American breed). It was a fun couple hour ride in a beautiful setting.
I’m pretty sure we hiked along the Minaret Burn Track. It was a really pleasant, easy hike with wonderful views.
So, in general, you should head to Wanaka. It’s relaxing and gorgeous. Great place to spend a few days.