Everybody's suggestions are great, here's a couple more (having recently traveled extensively through the Yucatan area):

Cancun - Don't stay on the strip (it's like Miami), stay on the Yucatan coast in one of the many places as it'll be more relaxing, less tourists and better service (my opinion).

Playa- it's quickly becoming a shopping/ partying place for all the people who stay on the coast (as it's "the" city to and visit that's outside the hotel premises on the coast). I wouldn't stay in the city as it's not that relaxing, but for an evening of shopping and dinning, it's great.

Isla Mujeres - My parents honeymooned here 35 years ago and I was just there a few months ago. It's still a small, relaxed, quiet island that's great for relaxation. There's only one all-inclusive hotel here (on a tiny island accessed by a bridge from mainland Isla), all the rest is small two-to-three story houses and hotels that makes this picture perfect town great for R&R. There's a nice hotel called the Villa Vera that's quiet and yet good service.

Snorkelling - A little further south from Playa (30 minutes in public transport - every 15 minutes) there's a great town that has fantastic snorkelling. Just enter through the back entrance (where the couple of tourist buses enter) and you'll pay less to snorkel in the same waters and have the same great experience. (I just took a cab from the highway and after a 10 minute ride he took me to the cheaper entrance for about 30 pesos (under $3).

X-Caret- It's a very nice place that has history and is very developed for tourists. It costs about US$40 -45 for the day (and it includes a folkloric night show demonstrating a bit from each of the 30+ states of Mexico). It's worth it for this only (the snorkelling here isn't that great as there aren't as many fish as above). NOTE - most tour buses LEAVE before the show starts - so either have your own rental car (which is safe in the Yucatan/Merida area) or arrange to have a taxi to drive you back.

Merida- a nice cosmpolitan city with great day trips to nearby fishing towns and beaches and ruins including Uxmal ( a very important and large city that was reconstructed three times). It offers a nice light and sound show every night at 19:00 (again - most tours will not stick around until then). If you only see one ruin, this is the one to see.

Chichen Itza - Nice and lots to see, but not as much as the Uxmal. If you arrive early, you can wait a line to climb the inner stairs (of the first pyramid - as the new one was constructed on top) to see the red dragon that lies there from many years ago.

Oaxaca - wow, this city was great with lots of culture and history. A few days just being inside the city (not including sorroundings) is enough to fall in love. There are nearby ruins that are on top of the mountain overlooking Oaxaca that are impressive. The food in the city is fantastic. The local dish - Mole - is a mix of chocolates and seasonings that will leave your mouth asking for more. My girlfriend and I took a local cooking class (from a local - not from the other lady who gears to tourists) and charged us about 400 pesos ($35) for about 3 hours. She explained everything in detail as she instructed us how to cook. At the end, we ate, took pictures and understood the recipe so well that we've cooked it here (in Toronto) a few times already.

From Oaxaca you can go by bus or plane to Puerto Escondido and enjoy a good beach (with much less tourism than the Yucatan), where diving and surfing is popular. Puebla is also nearby and worth the visit.

Baja - I haven't visited this area much, but it's known to have great cuisine, lots of shopping, lots of sightseeing and fishing. The two towns of Cabo San Lucas and San Jose del Cabo are the main attractions with the first being a more touristy upscale town and the latter being where the locals live and where there's more culture and cheaper shopping available.

DF (Mexico City) - This city, my birthplace, is fantastic, full of history, culture, architecture, food and ambiance. There's many places to see and do that you'll run out of time. If you only have a couple days in the city visit the artsy area Coyoacan where Frida Khalo and Diego's house are. Dont' forget to pop into the national palace and experience some of the greatest paintaings (that I've seen) that will explain the history of Mexico. Grab a tour guide at the entrance to understand it better. The Palacio de Bellas Artes (the national art gallery and palace) is another not to be missed place. The Zona Rosa (tourist area), Chichen Itza (one of the largest city's in Mexico with the moon and sun pyramids alligned with each one respectively).......

well this is a brief rundown.. let me know if you have more questions and I'll try and answer them..