The airport in the Bay Islands with the most service is undoubtedly Roatan (RTB). I second the suggestion for West End, though I have to say it was rather a backpacker destination when I visited (as a backpacker and diver) six years ago. They may have come up with some high-end options by now, but back then it was mostly hostels or low- to mid-range hotels.

I was there in August, and the weather was fine - though at the same time a hurricane was churning its way across Yucatan which could just as easily have turned south towards Honduras, so it all depends on your luck, I suppose.

EDIT: Oh, and upon reading Greg's trip report, I remembered something else. The bugs to worry about on Roatan are not mosquitos, they're sandflies. As the name implies, they're often found at the beach, and usually just before sunset. They don't carry any diseases or anything, but their bites itch like a &/(&%/(%$R.