If you're looking for a nice place to chill out in, don't visit Turangi! It's a working class town and a prison is located nearby, which brings plenty of unsavoury characters hanging around on the streets.
If you want to do stuff in Tongariro National Park, stay in Turangi, not in Taupo or one of the places to the south. Taupo is too far away and the places to the south are on the wrong side of it. I didn't have to pay for a single nights accommodation in a week here as we were invited to stay with some of the dodgy people we met in the town's single pub who turned out to be really great. However I saw a lot of younger kids who I bet wouldn't think much about breaking into your car and nicking stuff if you left it parked in the wrong place. The chinese place across the road from the pub does some of the best fish and chips in New Zealand (and I had a lot of fish and chips in New Zealand), well worth checking out. Lastly, the Tongariro crossing is of course an excellent hike, but also consider the hike up Mt. Ruapehu from the top of the chairlifts to the crater, it does involve climbing on snow but it's really not that technical or difficult. Me and my friend did it in trainers in less than three hours (make sure you pick a day with good weather though if you attempt with similar gear, and we were quite fit at the time), the view from the top and the acid crater lake are incredible, and the sliding back down on the snow (bring a plastic bag) was great fun. Also cool to know you are the highest people on North Island (unless there are rock climbers on the summit I guess). Also be sure to check out Lake Rotopounamu, which was probably the most tranquil spot I visited the whole time I was in New Zealand, incredibly friendly ducks too. Take swimming gear and they will swim with you.
Turangi is a killer spot for the serious outdoor enthusiast. Tongariro crossing (ranked one of the best day hikes in the world) is just up the road along with tons and tons of fishing opportunities. Just a word of warning, I heard about a lot of cars being broken into here so be mindful of your stuff, especially fishing equipment. The hostels are nothing special but they suffice well enough. Anything you can't find in Turangi, you can find in Taupo up the road. I suggest walking straight to the Tongariro river with a big tungsten bead hare and copper and chucking it into the Major Jones pool!