The first and only time I stayed in Key West was last year. We initially booked into the Wyndam Casa Marina, and the $400 room we were assigned
truly sucked. It looked like the room's last reno was in 1970 and the room smelled like sewage to boot. I understand some of the rooms at the hotel are nicer, but the place was fully booked and the folks at the front desk claimed they couldn't move us. We decided to walk, and the manager was kind enough to call around and find us a room elsewhere.
The place we ended up,
The Pier House Resort and Caribbean Spa was wonderful! It has a Gulf-side sandy beach (apparently the only authentic sandy beach in Key West) as well as a swimming pool, and it is very kid-friendly. It's right within a block of the main tourist strip, yet it's quiet. When I go back to Key West, I'll be staying there again.
Enjoy your trip!