I recommend you
research the available choices and make up your own mind about what you would find
interesting. My friend and I had slightly different impressions and preferences for the
various sites, as will you. However, if you want my opinion....
If you can only visit one site, Tikal would be a good choice. It was the only site that we couldn't see all of in one day. It is very spread out, exists in the middle of a protected biosphere reserve, and has several tall picturesque pyramids that poke up through the surrounding rain forest. (As seen in the first "Star Wars" movie.) The lack of civilized comforts at the in-park inns (you only get the bare necessities in your room, and only have electricity when they run the generator from 6-9pm) adds to a sense of adventure and "roughing it". You will encounter more wildlife here than at most of the other sites, and will have plenty of buildings and pyramids to climb on and explore.
Another good choice for top site would be Palenque. In the hilly Chiapas region of Mexico, the area is very lush and green, unlike the dry forests of Copán or Tikal. The Temple of Inscriptions with the famous tomb of Lord Pakal is an important highlight, and many other temples can be found in a beautiful forest setting. It's nearness to the ruins of Bonampak and Yaxchilán also means that you can visit three sites during your stay in the region.
The ruins of Copán in the Honduras are not as well-visited as the other large sites, but it has to rank as one of our top five choices. The huge ornate stelae and abundant architectural ornamentation made this site worth visiting. The new museum with it's full-size replica of a Mayan temple was worth the trip in itself.
Chichén Itzá is probably the most visited of the large sites, due to it's proximity to the mass of tourists in Cancún. It's hard to imagine a trip to Mayan ruins that didn't include a stop at Chichén Itzá, though the amount of people you have to deal with somewhat spoils the experience. (This is quite different from our visit to Bonampak, where we were the only two people there, not counting the guide and the guard.) The often-photographed step pyramid of Kukulkan and the famous round Observatory are required explorations for any Mayan enthusiast, and there are a number of other interesting structures as well.
I think Uxmal is every bit as impressive as Chichén Itzá, but being farther from Cancún it is not as crowded. The oval Pyramid of the Magician, the House of the Governor, and the Nunnery are magnificent examples of restored Mayan architecture. You also have the side benefit of being able to visit the nearby ruins of four other smaller Mayan sites.
Rounding out my list of recommended large sites would be Yaxchilán, a rarely visited site that truly lived up to my preconceptions of what it would be like to explore ruined Mayan temples in the middle of a lush rain forest. It is easy to get to from a day trip arranged in Palenque, and the required boat ride there helps give an "Indiana Jones" flavor. Just don't expect any gift shops, hotels, or fancy restaurants.
Tulum is probably the most crowded site, as hordes of Cancún visitors go there every day. The ruins seemed more "ruined" than I was expecting, but the view of the crystal-blue water it adjoins makes it a good place for postcard-type photos.
Cobá is a huge site (over 6000 buildings have been identified in the vicinity by satellite photography), but you wouldn't know it when you were there. Most of the ruins are buried under centuries of dirt and plants, and only a half dozen structures seem to have been unearthed, and even they are only semi-restored. It's worth a stop if you're in the vicinity, however, if only to climb the large but dilapidated pyramid known as Nohoch Mul (the tallest pyramid in the northern Yucatán).
Other sites abound, like Caracol and Altun Ha in Belize, Quiriguá and Uaxactún in Guatemala, and numerous others throughout the Yucatán. Find out how much time you can spend on your trip, and set your priorities based on whether you want to see the highlights of a lot of sites, or take your time and really explore just a few of the more important ones.