We have traveled extensively with our kids, who are now young adults. We live near Boston, but flew regularly to Toronto and Calgary and Mexico where the kids were little. We took them to London when they were 4 and 7. After that, we took them all over Western Europe as well as to Australia, Indonesia, Japan, China, Nicaragua, Costa Rica, Russia, Austria, Slovakia, etc.
Hawaii would be a lot farther than I'd be willing to do with a little kid. I'd pick a place that is easier to get to buy has good water and health care. Florida (Sanibel or Naples)? Costa Rica? Panama? Even Mexico at a resort that has good drinking water (I recall taking our not quite two year old son to the beach in Puerto Vallarta). We haven't done a lot of Caribbean trips (other than the Yucatan and St. Croix) so can't advise you there.
Each year, we now take a family trip someplace new and our kids really want to come with us. We now allow them to take a friend (BF, GF or just friend) and we will pay their ground expenses. The friends just have to pay their airfare.
By the way, it is a lot easier with one kid than two. We had a hiatus from trips (other than Canada and Florida for family) when the second kid was 1 until she was close to 5.