where do i apply for a Visa to china? I would be staying no more than 21 days. Im in United States

You should apply from the embassy or consulate of PRC in the United States according to where you live. If you can tell me which state you live, I can give you an exact answer.

I live in Rochester New York and need to kniow where and how to apply for an entry permit to PRC

You should apply for it at the consulate general of PRC in New York.
Considering your situation, you can apply for a tourist L type to enter PRC. You should first prepare the required documents including your passport and copy of its data page, the filled-out application form attached with a passport-style photo, and an invitation letter from your fiancé. And then submit your application to the consulate general to apply for it.