I have been at USF in Public Health for 2 years. I live in downtown St. Pete on the edge of the USFSP campus. I love being 2 blocks from the water, walk to the grocery store, bars, restaurants, parking isn't awful, always things to do. Tampa, near the university, kinda sucks. Its busy and stripmall after stripmall. And traffic can be ridiculous, granted commuting across the bridge can be a nightmare. I would think if you need to be on campus 4+ days a week, I would tend to live in Tampa somewhere. You will not lose 45-60 mins twice a day and you can go to more social stuff. I chose to live in St. Pete because my girlfriend got a job at the local hospital and I knew people here.
The weather is awesome coming from Ohio. April-September expect it to be very humid, hot (90-95) and rain daily. Heavy rain. September-Dec (60-70s) cools off and humidity drops out. Jan-March is similar to Sept-Dec but cooler (coldest has been 36, high has been 88). Sun nearly every day. Add 5-10 degrees if you live near the university and away from the water. And there are lizards, ants, cockroaches, mosquitos, noseeums, and spiders everywhere. Its a fact of life here. I have a newer apartment and I havent seen any of the aformentioned pests inside. I lived in a house last year and we had minor roach and ant problem (they are naturally occuring in the sandy soil). We mitigated by keeping it clean, and taking out trash often and using traps. I havent seen a ton of spiders, but when I do, those things are huge! I would worry most about lizards (outside) and roaches (inside).