The sights most Cancun visitors want to see are the beach and the ocean. That's probably a good thing, because there aren't many other attractions—no casinos, few historic sites, no public parks or gardens, and no historic neighborhoods.
The hotels themselves are attractions. We recommend stopping at some of the more outlandish ones along the Hotel Zone to have a margarita and marvel at the architecture—you'll find variations on Miami Beach and Las Vegas, along with Mexican themes. The buildings are a dizzying melange of styles, from block-long pink palaces with towers and cupolas to sleek, mirrored pyramids with huge, tree-filled atriums.
There are a few escapes from the resorts, however. Ruinas del Rey provides a decent, if brief, introduction to the ancient world of the Yucatan, especially if you can't make it to one of the bigger archaeological sites. The shores along Nichupte Lagoon (particularly the southern end) are less developed and more protected from the open sea. They're rich with bird life. Most hotel travel desks sell lagoon tours or something billed as a "jungle cruise" that's actually a boat ride through the lagoon to look for tropical birds. These are frequently bundled with a stop for snorkeling in the Caribbean shallows.
For anyone interested in Mayan history and culture, a visit to one or more of their ruined cities is essential. Tulum, on the coast south of Cancun, is the closest, but tends to fill up with coach parties. Chichen Itza is the most famous and a World Heritage Site, and Coba, the least developed of the three, is in a shady jungle, making it ideal for an afternoon visit. Local tour operators offer convenient packages, or you can hire a car and organize your own visit.