This beach is amazing. The water is so clear and the sand is very clean. It's 1.5 hrs from Mobile. Parking is free. There are lots of gift shops and restaurants, and if you want to be in a quieter area, just keep driving west on the island and there are many parking spots and public access beaches. If you want to go on the pier, I think it costs around $3 a person.
Okay so this is a weird recommendation, but if you like a good thrift store, this is the one for you! It's got a bunch of nice clothes and furniture and random lil things to look at. I always find something cool when I go.