This national park encompasses three large volcanoes in the center of the north island an hour and a half south of Taupo. Tongariro is most famous for the Tongariro Alpine crossing, billed as the best day hike in the world. It’s a challenging 12.5 mile one way hike up from forest through lakes, volcanic flows, alpine scenery, and hot springs. It looks awesome but unfortunately when we were there the mountain was fogged in and raining, If you do go, start early, You can catch a shuttle from Turangi a small town on the south end of lake Taupo that will save you a lot of driving to the visitor center at Whakapapa village (where you can also arrange a shuttle from here).
If you are not up to 12.5 miles of volcano or the weather is lousy consider a great hike to Taranaki falls (about two hours return)