My husband and I first considered DR when we were looking for a vacation place in Caribbean. We wanted to go to Sto. Domingo so that it would be accessible, if we were to take a city tour. But then I read reviews that the city could get pretty rowdy at night and the resort that we found did NOT have good reviews. The pictures from some of the previous guests there were pretty awful. Dirty bathrooms and all.
Most of the suggestions I read led to La Romana, saying that the place is family-oriented. But with just my husband and I, we were not really looking for a family-oriented place. So we skipped DR.
We ended up going to Jamaica because we found a better deal. We were not particular with the location, we just wanted to get away over the long weekend.
Cheapcaribbean.com has good deals, if you are looking for a vacation somewhere in the area. And to be honest, not that I'm promoting it or anything, if we were to go to Caribbean again, I'd go to that website first. When we were in Jamaica, some of the guests booked their vacations from AppleVacations.com.
As for the search -- We are pretty cheap
And we do not have many restrictions when we search. As long as we get to see the place (some tours), it's safe, there's decent food, and booze -- we're good. Your case is definitely different because you have a young one. So what we did was to look for a good deal online and did a h3ck of research about the resort in various websites. We read reviews, lots of them! Even small ones from answers.yahoo.com, I was reading those; just to check if there's anything alarming.