The riding around the coast is not much to speak off. Flat roads, lots of congestion this time of year (tourist) and hot and humid above belief. The beach itself is great- white sands, clean warm, water, oughta be the focus of the trip.
Put a bunch of tourists in a unvented, metal building on a 100 degree, with matching humidity, and you get the idea. This is not the time of year you'd wanna do the walking tourist stuff, the battleship is best left for the fall and winter.
The air museum is in Pensacola, and worth a visit, but over there and back from Mobile is gonna take ALL day, and I'd be reluctant to give up a day at the beach to do that, but that's just me.
Althought I do it, I don't enjoy riding as much this time of year in Alabama. I rarely take off all day for a ride in August, just too hot. When I do go I tend to keep it under 100 miles and dream of fall and winter.
So if it were ME, I'd hang around the beach, sip what I like the most, swim, take the wife shopping to the nearby stores, eat some good seafood and relax knowing we don't really hafta to be anywhere. We go there 4 times a year, but only once in the summer. I'd leave the ST at home it would be a lot of trouble to trailer it all that way, and probably not have a good time riding it.