Birmingham is a car city. The main sights are not concentrated enough to walk between them without considerable effort, and public transit is minimal. Renting a car or using rideshares is the practical choice for most visitors.
The one exception is the Civil Rights District, where the Birmingham Civil Rights Institute, 16th Street Baptist Church, Kelly Ingram Park, and the Birmingham Museum of Art are all within a short walk of each other. Park once near Linn Park and walk the district on foot.
For longer trips — Barber Motorsports Museum, Red Mountain Park, Rickwood Field — you will need a car or a rideshare. The airport is served by a dedicated shuttle service and all major rental car companies.