we've done Egpyt, The Maldives and the caribbean at Xmas and all three would fit the bill depending on budget. The North Coast of the Dom Rep would suit very well as there are a few things to do and the hotels are very family friendly with loads of activities for big and small kids alike. Would definitely reccomment either the Riu or Iberostar chain of hotel in either the Dom rep or Mexico (not Cancun) - both are first rate.
Yea, Playa del Carmen, great - on the beach, the ferry to Cozumel 20 mins walk away and the temples near by. Plus it's enough commercial to take a nice walk down the 5th Avenue (buy from the Mayan women on the streets) but pretty laid back, not like Cancun. There it's all concrete blocks on the beach. (bit like Torremolinos for the US)...
You can even go into the Walmart further into town, which is great for the US/Mexican "Tesco" experience and they have some nice cheap tourist tat - notebooks/mugs/coasters with Mayam temples on them - the Mexican supermarket next door is even more interesting for the local culture.
For teenagers it's great too (I had mine with me, he got invited out by the receptionists...came home at dawn -it was Ibiza in Central America...lol)