Med student in need of housing for 5 weeks with pet cat.

Hi! I am looking for a place to stay from the end of July to the end of August with my cat, Hank. He is 14 years old, sweet and sleeps most of the day. He loves pets if you want to give them. I keep everything very clean and am respectful of property. He is also content with staying in one room if that is preferable. He does not jump on tables/counters. I am having quite a hard time finding an affordable place to stay that is ok with cats. Any recommendations would be great!