Mel Fisher Museum (treasure)
Hemmingway House
Lighthouse Museum
Southernmost Point
Butterfly Museum
Mallory Square at sunset (circus acts on the boardwalk!)
Sloppy Joe's
Aquarium
Kermit's Key Lime
Glass bottom boat ride over the reef
All aboard The CONCH TRAIN!
And, I second Blue Heaven (doesn't have to be breakfast. Actually, I prefer dinner after dark, which will be early in December. I prefer the colorful night lighting, as this place is like eating in somebody's back yard, under the trees. Very unique.)
and the Fast Cat to the Dry Tortugas - awesome trip!
(continental breakfast on the way out, guided tour of Ft Jefferson, box lunch at the fort, time for snorkeling, relaxing ride back to Key West - full day!)