I would go to Mexico. We traveled extensively when our kids were that age and Mexico was always a great trip. Pick some place in the Riviera Maya and plant yourselves for a week. Gorgeous beaches, good food, nice accommodations, direct flight, same time zone, etc.

We took a 3 month old to Hawaii from Chicago once and it was a wonderful trip but the flights were long.

We took three 2 and 3 year olds to Key West one year. The drive to Key West is long after a flight and all the hassle of shuttle to rental car place, installing all the car seats and then the drive. It is 4 hours if there are no accidents but can be longer. There is very, very little to entertain young kids in Key West. Fortunately, our house had a pool and we went to the aquarium several times.

A condo in the Caymans was another good trip with kids that age. We could hang on the beach while the kids napped in the condo just steps away.

Good luck planning.

We fly from Minnesota to Mexico every winter and stay a month. Its 3.5 hours non-stop to Cozumel. You can do an all-inclusive resort (I hate them) or rent a condo or pick a small boutique resort. It will be warm - guaranteed. Cozumel is a wonderful island with great food, shopping, sports and lots to do. They even have a rental for all your baby needs. The Mega grocery has all the US brands of food you might need for the little one, too. Cozumel is a very family friendly location.

The virus you are concerned about is not present in any part of Mexico.

http://www.cdc.gov/chikungunya/geo/index.html

Baby in Paradise rental:
http://www.babyinparadise.com/

The whole Riviera Maya area of Mexico would be great - lots of warm water, friendly people, interesting places to see, and very safe. Have you looked at locogringo.com?

Another vote for the Caribbean coast of Mexico. It's not as long a flight as Hawaii, and will actually get you into warm/hot weather, which none of your other ideas really will.

I do also, it's just a bit over 3 hrs, and the Rivieria Maya is a great place with children. And definitely warm and fairly cheap compared to other places you might go. You can fly to Cancun nonstop from NY in only about 4 hrs, then rent a car or book a shuttle service to some AI south of there or something like that (such as in Playa del Carmen or not far from there).

You could go to San Juan, also, I just didn't like it as well as Riviera Maya and it is more expensive, also.