Most university-level Chinese courses are pretty much the same in my opinion, so I would personally optimize your plans for whatever environment is going to motivate you to do things in Chinese. For me this would mean a decent-sized university (more students mean more social activities and stuff on/around campus) in a part of the country you would like to live. Pollution is a real concern if you are even thinking about staying through the winter. I would personally go south/southwest to Hangzhou or Chongqing rather than risk Beijing or Harbin at this point.

In major cities AirBNB rentals tend to be more expensive than hotels or hostels. If your school is providing you with an actual study visa (i.e. not a tourist visa) they may be able to set you up in a dorm -- something that will also encourage you to get out during the day. Apartments in 2nd tier cities will be available for 500 USD / month or less too, so as long as you have a place to stay for a week or two after arrival, this is something that you can productively leave until you get here.