Hi Dave,
My wife and I did a similar trip two months ago with the same goals in mind; see the museum and hit the beach. We skipped the big airport (Pensacola Regional, PNS) across town and landed at Ferguson (82J) instead. Methinks it was a good choice.
It's a nice little airport, tiedowns or overnight hangars are available... we did two nights in the big hangar, $20 per night. Not too shabby. Nice people and great service. I had called ahead the day before to ask about hangar space and rental cars; as we rolled to a stop on the main ramp they were opening up the hangar for us and the rental car was waiting before I had the ship secured. They're very close to the Navy museum and have connections to some condos if you wanna stay in the Perdido Key area. We spent most of a day at the museum and it just wasn't enough time to see everything... but the good thing about that is now we have to go back to see the rest of it!
http://www.fergusonairport.com/
http://www.airnav.com/airport/82J