Generally speaking, Jeff is correct in that great Caribbean food is mainly found in places where an indigenous population still exists and outnumbers the tourists. However, those places may not be compatible with a family vacation with members who may or may not be adventurous. I think you need to realistically consider how much time your family will want to spend on or off-resort. You could stay in the most wondrous food destination (see Jamaica below) but if your family doesn't want to wander off-resort, then your food experience will be greatly diminished. You also should consider how much trouble it is to go off-resort. If you have a car, it might not be a problem. But sometimes, the trouble it takes to go off-resort may not be compatible with some people's idea of "vacation."
Some examples:
Jamaica. I greatly enjoyed my time in Jamaica (Negril), and have no reservations recommending that your family would be happy staying at a more upscale resort in the Cliffs. I personally recommend Moondance Cliffs. I would also tell you that you can have some wonderful food at some of the shacks nestled along the Cliffs. BUT -- this is a consideration when you're with family who may be sensitive -- the native islanders even more so than the tourists will be smoking weed around you. Some of these shacks make food to order depending upon what they have available. As in, you show up early in the day to order your meal for that night or the next day. They'll either go out and fish for it, or they tell you they have goat or chicken, and if you look behind the shack, you'll see a goat and a chicken, and when you return, either the goat or the chicken will be missing. The restaurants won't be well-appointed, and most of the time, you'll be eating outside at picnic tables. There are some exceptions, more traditional restaurants such as Rockhouse, but the food is sanitized for Americans, Brits and Germans. The other thing is that you'll have to deal with people approaching you to peddle goods, some of which are drugs. I definitely wouldn't suggest staying on the Beach in Negril, where the constant peddling is likely to rankle older members of your family. (It bothered me.) But even if you are satisfied spending most of your time at the resort, if you need cash, the ATM in Negril is a hold-your-breath and hope you're not robbed experience. My cab driver insisted that he accompany me every time I hit it. (I'm pretty well-traveled and not easily scared off, but when a guy is standing at the bar across from the ATM with a machete, yeah, I think it's not the safest place.) (BTW, you'll need to have either a car (they drive on the left) or a regular driver to ferry you up and down the cliffs.) Having said that, the natural beauty is stunning, the music is great (get used to hearing Bob Marley), and the food's good especially if you eat at the roadside shacks, but there's a bit of risk there that you might not be willing to take. Oh, the 1.5 hour drive from the airport in Montego Bay takes you past a lot of impoverished towns, goat-filled hills, and stray, starving dogs. Not for the sensitive.
Grand Cayman. On the other end of the spectrum is Cayman. All foodstuffs are flown in (mostly from Jamaica, I'm told). Food's bland, uninspired for the most part. And it's expensive given it's position as a toilet for offshore money. But, it's safe. It's easy to get around. It's clean. I stayed at the Ritz-Carlton, I would go again just for the comforts of that resort even if it meant sacrificing great food. The beach is incredible. Very sandy, clear, blue-green water.
Puerto Rico. Puerto Rico might be your happy medium. I didn't stay in San Juan (wouldn't want to, it's too urban), but there are other areas that are more secluded, prettier and less congested. There is plenty of good food if you go off-resort. (See this
post.) If you rent a car, you'll get around easy. I stayed in Fajardo at El Conquistador, which was located near my scuba diving shop. The resort didn't have great food, but my scuba diving leader, a native Puerto Rican, offered to act as guide to local food. Most people speak English, and I never felt unsafe there. In terms of natural beauty, it's not up there with other Caribbean destinations but it's also nothing to sneeze at. You could also consider the less congested western half of the island, or Vieques, a small island off its eastern coast. You can take a direct flight to San Juan from Chicago; that's a plus.