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Hey there!
Last November my boyfriend and I booked a flight and hotel package for Havana and I would highly recommend it. I found that Havana wasn't heavily tourist oriented and offered me an authentic experience while I still felt safe (when I wasn't lost). We stayed in the Islazul Caribbean and though it has a 2-star rating, we had a wonderful stay! It was within a few blocks of the capital building, the harbour, and Old Havana. The hotel was right on Paseo Del Prado which is a road built by the Spanish to mimic one of the main boulevards in Madrid.
My travel experience in the Caribbean is limited to Havana, but I hope this helps a bit.
P.S. Our entire trip cost us less than $1200 each!

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By mid-November the rainy season is usually pretty much over (not that the "rainy season" is all that bad) and the chance of strong storms is even lower than usual. That's pretty much true all over the Caribbean, so you don't really have to choose your island based on weather. If you really, really want to play it safe, you could go to Aruba or Curacao, which are "below the hurricane belt" and arid.

As for all inclusives, it all depends on your preferences, but I'm no fan. I like to leave my hotel and explore, eat where and when I want to, etc. I think an AI plan just further tethers you to the resort, and I don't think they are usually all that cost effective either.