Nozawa Onsen would be great choice, the town has a great atmosphere and onsens are abundant. There are places closer to Tokyo than Nozawa that you could go to, but Nozawa is good because you get a traditional village experience as well as excellent snow. Generally, the cheaper accommodation doesn't have their own onsen. This is not too much of a problem because there are 13 free onsens around town. The whole village is really close to the ski resort, so anywhere in town is pretty convenient.
There is some pretty cheap accommodation on this website http://www.naganogo.com/nozawa-onsen-accomodation/