Case Western is an excellent medical school and you will have more flexibility with regards to matching to competitive specialties and to competitive places than UAB. I would go to CWRU.
Edit: I also grew up in Cleveland and went to school in the South. The climate is definitely better in the South, but the location is what you make of it. I personally think Cleveland is a great place and I think the downtown area is being revitalized in recent years. They are full of arts and culture (Rock and Roll hall of fame, Cleveland Art Museum, Cleveland Orchestra (one of the original big 5 orchestras)) and sports (Cavs, Cleveland Guardians). Besides that if you drove out a little, there are plenty of parks if you are an outdoorsy person. Just my 2 cents 🙂