It's best to know the situation so the question isn't that stupid, don't worry. Having recently undertaken a similar journey as outlined above, with an Irish passport, I can happily confirm that there is no special visa requirement. The plot thickens though when we move away from you, as a person, and onto your baggage, as a vehicle for trafficking contraband.
As for Mexico City, it's well worth a visit, very nice, vibrant city centre. I find virtualtourist.com to be a useful repository when it comes to deciding on what to see and do. When it comes to Cancún my advice would be to wear sunscreen and to visit a club called Coco Bongo(not at the same time particularly). Its open seven nights, and is always busy. The cover charge is expensive, $45, but there is 'free' drink thereafter and given the mania you will experience the seemingly steep price is best overlooked. When I was in the area I stayed on an island off-shore so I can't recommend any hotels I'm afraid. Buen viaje
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