Florence, Alabama feels bigger than it looks — a friendly, affordable riverfront university city with a lively arts and music scene (Muscle Shoals recording legacy), a walkable historic downtown, regular live music, good restaurants and parks, and easy outdoor recreation — all the variety that makes multi-week stays enjoyable rather than boring.
For occasional big-city options, Huntsville (tech, museums, nightlife) and Tupelo (regional shopping/entertainment) are both within about 75 miles, so weekends can be varied and convenient.