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Going to Cancun.
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For a side trip, check out
Tulum (1.5 hours from Cancun) or
Chichen Itza (3 hours from Cancun).
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I definitely recommend the trips to the Mayan ruins. If you are going to be in the area for a "while" and you like Mayan ruins, I'd also recommend trips into Belize and to Tikal in Guatemala. For real adventure, take the river route into Guatemala after a trip to Palenque in Chiapas.
Closer to Cancun, Cozumel is pretty cool, and Isla Mujeres is laid back. You will get a lot out of those trips if you are a diver, but if you are a diver then you already knew that.
Ciudad Cancun is not worth the short trip unless you have a specific reason for going there. Also, Yucatecan food is not very good in my opinion, but you will find many American chain food restaurants in Cancun.