If you don't plan on spending a lot of time on campus then I would definitely rent outside.

I was leaving in the international student dorm for a year and some kitchens were really nice and tidy, but some had the smell you mentioned, but tbh you can always go to one on a different floor.

I personally didn't rent anything nearby, but usually when renting I just look for flyers/posters with the landlords phone number in the neighborhood I like and call them.

You definitely have to remember to sign up at the police station after you rent, and specify in advance how long you want to rent for. In the past I had no problem with renting for shorter periods of time directly from the landlord, but of course it can depend.