Cancún is a planned tourist city on Mexico's Yucatan Peninsula. It is a popular vacation spot on the Caribbean coast. There is much to do in the city, and if you're willing to take an hour or two bus trip, there is more to explore than you could possibly fit into a single vacation.
Cancun itself was built on a site selected as the ideal spot for a new tourist development by the Mexican government. A story that it was chosen by a computer is not true. The state of Quintana Roo was still a territory and this area had few inhabitants when Cancun was built. The Cancun hotel zone is almost entirely built around the tourist industry. It abounds with all-inclusive resort hotels. Stay here only if you don't mind spending your vacation with many other tourists.

Downtown Cancun, especially once you get away from the ADO bus station and nearby hostels and hotels, is a real Mexican city. If you have an early flight from Cancun, staying in the downtown area is not all that bad.
Those mostly seeking beaches, scuba diving, or who are a bit adventurous can easily find rooms on equally beautiful and less crowded beaches somewhere an hour or two drive south along the coast for much less than the cost of major Cancun hotels. Some Spanish language skills may aid in finding better deals. You can rent a car, or take the bus to Puerto Morelos (about 20 minutes) or Tulum (1 hour). Playa del Carmen (45 minutes, MXN$80) is between the two, but caters to the all-inclusive crowd. Taxis are also available.
Those looking for a base of operations who want good or luxury hotels and the advantages of urban life but prefer more local flavor may wish to stay in the Yucatan's main city of Mérida; many international flights in to Cancun continue on after a stop to Mérida's international airport.