Dominican Republic, Cancun (including Playa Del Carmen) and Cozemel all have lots of places suitable for the budget minded family. Several other destinations may also fill your requirements but without more information it's difficult to make meaningful recommendations.

Where are you flying from? Do you want a destination you can reach non-stop from the gateway city nearest your home or are you willing to take one or more connecting flights? (For a long weekend you probably should consider going someplace you can get to in the least amount of time). How old are the members of your family? Do they have any specific interests? What is your definition of "family fun on a budget" - that's a vague term - it would help if you could give an actual dollar range for accomodations, meals and transportation?

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