Rent Bikes and you will have the best of all worlds - Calm Caye Villa is super, and there are lots of places to eat within walking distance from it - Rojo, Mambo, Belizean Shores, Rendezvous and Sundiver is almost next door.
You can also hire a private chef (yum!) to do gourmet meals in your home (he washes dishes afterwards too).
The bike-ride from CCV to Palapa is about 15 minutes and is fun.