Some of your best sources for affordable family vacations to Central America are travel aggregate websites like Travelocity, Orbitz, or Hotwire. For example, recent Travelocity listings offer several trips to San Jose, Costa Rica, that include flights plus six nights' hotel with advertised rates around $200 per person.
Panama, the small Central American country that hosts the Panama Canal, has been creeping onto the tourist destination radar for a few years now. Political stability has brought relative safety to this country. Casinos, beaches, and a variety of resorts compete for your family vacation dollar. On Orbitz, you can compare Panamanian vacations that include flights and hotel for about $400 per person.
Occupying the northernmost spot in Central America, and part of the Yucatan Peninsula, Belize has been drawing crowds from America and Europe for a while now. Websites like BookIt.com often offer beachfront luxury suites for less than $200 nightly. Since it is slightly more developed in terms of tourist infrastructure, you will likely spend a bit more traveling to Belize, but it's still a deal compared to United States prices. As with all the Central America vacation spots, expect plenty of sun, sand, warmth, mountains, hospitality and historical side trips.