I've been to the Keys in October several times and was run out by a hurricane once. December in the keys will be considerably variable in December, and you will have to put up with some of the well healed snowbirds that flock down starting about then. Some days will be nice and warm and some will be slightly cool but certainly not cold. Pop up rain showers are possible. If you are a boater, the wind can be a factor; some days its calm or gentle breezes, and some days its a steady blow, that makes for rough seas.
We like staying in the Tavernier/Islamorada area. It's not too far down the Keys but still and easy 1 hour 45 minute drive to Key West, (or Key Weird as some call it.) The Keys only has a few beaches scattered up and down its length, the rest is rough shoreline or full of seagrass. Last year some friends went and said the dead sea grass and sea life piled up on the Atlantic side shores stunk so bad that they left and came home early; so get a reading on that before you commit to specific lodging.
Plenty of open air bars and restaurants scattered up and down the Keys.
HTH