Whakarewarew Forest aka The Redwoods in Rotorua is a must do. You can pay for a shuttle (Southstar Shuttles) for a day and there’s a good mix of tracks. It’s very flowing, the soil has excellent drainage and is grippy as anything. Rotorua also has a gondola, lots of food options and nice to relax in the spa after a day riding.
Taupo has a few options the best day ride is the W2K trail from Kinloch. It’s a there and back, but you can arrange a water taxi to take you back to the starting point. There’s a cool little trail nearby called Craters of the Moon that takes in some of the thermal sites. Wairakei Terraces or DeBrett’s spas are good for post ride relaxation.
If you’ve got time and want a real adventure then The Old Ghost Road is as good as it gets. This is a tough back country ride following an old gold miners route in to the mountains.
Queen Charlotte track in the Marlborough Sounds is a pretty special ride.Very scenic, opportunities to stop and have a swim/kayak. Nice places to eat and stay along the route.
Nelson area has tonnes of riding, The Heaphy track in the Kahurangi being the most famous. This is only rideable in the winter months from May-Nov and you may have to book a huts in advance if you wanted to stay overnight. It can be done in a day. You can even get a small plane to bring you back to the start. Great beer in Nelson (it’s where all the hops are grown) and normally good weather.
https://www.newzealand.com/int/feature/top-mountain-biking-tracks-in-nelson/
Then you’ve got endless trails in Queenstown and some nice ones in Wanaka – Dean’s Bank track is nice wee ride.
Christchurch has a bike park and Gondola in the Port Hills. Craigieburn not far from Christchurch is a brilliant ride.
There’s tonnes of riding in New Zealand. You won’t be disappointed!