only places I've stayed there is cheap motel way far end of Duval, the youth hostel for long period, and with friends who had room at Pier House for New Years 2000! :00hour
Pier House is definitely the place to stay (preferably in summer when half price...).
Key West is a coral island, and hence all beaches are scarce and little man-made things. Pier House has their own private beach right at the foot of Duval Street! Just bit over one block stumbling distance from Captain Tony's Saloon and Sloppy Joes bars. But they have thier own nice little bar right on the beach too.
My favorite drinking places were the funky old
Green Parrot Bar, the sort of place you'd only find in Key West. And fine elegant, beautiful "The Afterdeck" at
Louie's Backyard--sit on stool and listen to waves and watch ocean and pier (tho in day all you hear are dogs splashing and barking at the dog beach next door).
also fun to drink at that bar (can't recall name) on fishing wharf late in day and see what fishing boats bringing back.