Another option is Ft. Pickens-Gulf Islands National Seashore at Pensacola. The drive is same distance as to Dauphin Island. I have been there several times and the beaches are fantastic, and again, some good seafood eating (I am not, however, a seafood person).
Lots of stuff to see and do in the area, including the Naval Aviation Museum at Sherman Field-Pensacola NAS. Near the museum is Big Lagoon State Park which is good camping and walking trails, and easy access to Johnson Beach, also part of the Gulf Islands National Seashore.
If you have an America the Beautiful Pass or Senior pass, you will save the $20 fee at Pickens and Johnson Beach.
Charles