Lets see what I can come up with off the top of my head.
If you want to spend the whole time on the beach then consider a condo or beach house on Fort Morgan Drive west of Gulf Shores, that will get you out of the tourist trap. But if you want to be more strategically located to tour more things in the area then consider the Grand Hotel at Point Clear in Fairhope. Point Clear is about half way up Mobile Bay on the East Shore. Beautiful grounds, good accommodations, civil war history, spa, golf course, great dining. In Fairhope shop at the arts and crafts stores, walk the city pier and walking path along the bay, eat at the Yard Arm on the Pier and the Wash House south of the Grand Hotel. Unfortunately the Old Bay Steamer has closed now though. Be sure and walk the board walk along the bay south of the Grand Hotel grounds and look at the Antebellum homes and huge live oaks.
Shop the Tanger Outlets in Foley, eat at Wolf's Bay while there. Stop off on the way at Week's Bay Reserve and walk the boardwalk through the salt marsh.
Travel back to Mobile and tour the USS Alabama Battleship, book an airboat tour of the Tensaw Delta, walk the boardwalk at Meaher State Park, Eat at the Original Oyster House on the causeway.
Travel to Gulf Shores and walk the state pier at Gulf State Park, shop the strip, get a cheeseburger in paradise at LuLu's (Jimmy Buffett's sister) might get lucky and see him there, catch a concert at the Warf or the Hangout.
Travel to Fort Morgan and tour the grounds, imagine what it would have been like being garrisoned there in winter, take the automobile ferry across the mouth of Mobile bay over to Dauphin Island and tour Fort Gaines on the west shore, imagine being on a ship under crossfire from the two forts, then drive on to Bellingrath Gardens and tour the gardens, book a dinner cruise on their paddle wheeler.
My recommendation would be to go in May.
Click here for my pictures from the Grand Hotel and around the area.
http://s1112.photobucket.com/albums/k495/STCB-Photo-Archive/2008%20Grand%20Hotel/?albumview=slideshow