Beaches in KW are basically on the Atlantic Ocean side between the Southernmost Point and the airport. As far as those go, the Casa would be your best bet. I think the Pier House has a small, private beach, but I'm not 100% certain since I've never stayed there, but friends who have did enjoy the hotel. If you get a harbor view room, or one directed away from town, things should definitely be nice and quiet for you.

If you'd like a nice B&B a couple of blocks off Duval on Caroline (so no beach), in a nice place full of character and a great staff, my plug is for The Cypress House. I've stayed there several times and always enjoy myself there. If you have any questions please ask.