You have plenty of options. To get a first idea look at this ethnolinguist map of China (courtesy wikipedia) and that is far too large-scale to map all the minorities that are out there.
A comprehensive answer is out of scope so below I will give you some ideas. In any case you could either get on an organized tour or organize your travel by yourself. For the latter case the only guidebook I can recommend is the Lonely Planet, it's worth its price for this kind of endeavor.
- Xinjiang is a huge province in the Northwest with a muslim majority population. Kashgar had a great original feel three years ago. From there you could make a trip up the the Karakorum highway to the Pakistani border, where my hostel was able to arrange a stay in a defs not-Han yurt at Kahu lake. Plenty more options but note that cities are changing a lot so do some research on where you go beforehand.
- Tibet (Xizhang) requires some ever-changing permits but note that large parts of Qinghai province as well as Gansu, Sichuan and Yunnan are Tibetan and you can find a very original feel here.
- Read up on Southern Yunnan in your guidebook and you will find many destinations, e.g. the stunning rice terraces of Yuanyang.
- Inner Mongolia: haven't been but must be on this list.
This list could go on forever. Get the guide book, start reading and you will find more destinations than you can possible travel on your visa. If you are worried about Han-domination, it helps to get off the beaten track, avoid cities and major tourist attractions, wander around places and stay in places that would otherwise only be a day trip. You will still find Han Chinese people there but it does not necessarily mean that you cannot experience the local culture/feel/whatever it is that you are searching there.