I am a USA citizen trying to find the most affordable way to live in Kunming with the tourist visa. Is it possible to legally get a long term apartment contract with the tourist visa? I intend to stay at the same place for at least 6 months, but I will need to do a visa run. At the end of February I can convert the tourist visa to a student visa, since that is when the semester begins. But I want to move to Kunming at the beginning of November. Is this possible?

yes.

You could even rent an apartment or five without any visa, the landlord is not responsible for this and will happily take your money.

Depending on your school try to negotiate with them to sponsor your student visa from earlier on, you can then convert to a student visa in KM.

this is what I did, I came to china with only a tourist visa, found a chinese person looking for a roommate. You will have to pay a one month deposit, and then I also paid 3 moths up front. Sometimes you pay for the whole period up front. The lease will be for atleast 6 months unless you take over some former roommates spot. But the rent is cheap, mine only 650 kuai per month. Awesome