Bonaire: out of the hurricane belt and plenty of diving. Think of it as a "liveabord" without the boat!
I hate to sopund like a broken record and I haven't dove everywhere in the world---yet---, I'll second Bonaire.
I've never been there in November, but have in September, March and January. Water temps have never been below 79 degrees and as high as 84 degrees, so a 3mm might do year round. Viz usually is about 80', sometimes more.
What do I especially like about Bonaire. The list is long, but I'll try to be brief. The reefs are pretty pristine as the whole area is a marine park. You have the freedom to dive when you want, where you want, and for how long you want and as many dives a day as you can handle. Going in from shore you'll see stuff as shallow as 7' and as deep as 100' so you get to dive your own comfort level. You're never more than a couple hundred feet from shore, with no currents, so you'll never get "lost at sea". Lots of marine life and all you have to do is slow down and look for it (if you need fins you're going too fast).
There are lots of resorts at water's edge and most have a "house reef" that is just a continuence of the whole reef system, with very easy access. Comparing the price of boat diving most other places and the amount of dives you can do Bonaire might be cheaper than places like the Keys, and with Nitrox a free upgrade at most places there. YES, you can hire a guide if you wish, but frankly, a couple dives on the house reef would show you pretty much what to expect almost on any of the reefs. You can mix the shore dives with a couple boat trips out to Klein, a little island a few hundred yards off the shore, and this is probably not a bad idea as Klein has it's own little wonders.
You have time to do some comparison shopping so I'll mention this website---www.bonairepros.com. Although I'm not advertising for them it's just a site that shows several options of different resorts. These aren't the only places nor all the available packages, but should give you a start.
For what it's worth I've dove off Key Largo and Palm Beach area. I also have been to Bonaire 6 times in the last 4 years; trip #7 coming the end of September for two weeks. There really is no comparison. After having dove a few of places throughout the world, such as Fiji, Philippines, Curacao, Bonaire, Cozumel, Roatan, and others I'm not all that impressed with the Keys anymore. Of course, I can afford to go places, but if the Keys were all I could do I'd have to say that it's better than any of the local quarries here in Pa, which I do not dive but once every couple years.