I have brought my ride to the Keys four times over the last several years. Twice in Jan (because that is when I have time to do it easily), once in Mar/April, once in Jun. The weather was dang raw in Jan. Better weather than anywhere else on the east coast, but still not great. Cold fronts would come through and it was chilly and windy. Mar/apr was really nice. Jun was just dang HOT.
We occasionally anchored out, but anchoring around KW can be sketchy. You can feel like you have a decent bite, but there can be a relatively thin layer on top of the cap rock and once it starts to blow, off you go! The VHF goes crazy with dragging boats when a squall line comes through.
We stayed a bit at Garrison Bight at the City docks, that was not too expensive and they had plenty of room. I'm sure it varies, and that was several years ago, could be full now. Really need bikes if you are going to go anywhere interesting as they are long hikes.
A few nights we splurged and stayed at A&B docks downtown. Expensive, but fun. Only way we got in there was someone canceling out and they knew we could jump right in.
Spring is really nice weather. Fall is really nice too, but at risk of cyclones. Winter is raw but only when fronts make it through (some winters are mostly free of fronts, some winters they seem to come every week). Summer it is just dang hot, not so much the air, but the sun is intense. Walk out of the shade and sizzle!!
We only got a mooring ball in Marathon, that was pretty nice but not as much to do there as in KW.