Hi Jill, You would probably be looking at Gulf Shores or Orange Beach. While I consider Fairhope to be close to the gulf beaches, (thirty minute drive most days), I think you would be more interested in Gulf Shores or Orange Beach.
I have lived in Fairhope my whole life, and I love Point Clear and Fairhope. All the amenities you list are there, as well as down by the beach. I consider Fairhope and Point Clear, well heck the whole eastern shore, to fit your bill and be close. Depends on what you prefer. The Eastern Shore has tons of water activities, and if you have a boat, then all these communities are boater friendly, with public access, free launching and convenience.
If you want to chat, please feel free to call anytime.
Coldwell Banker United Realtors - Daphne