Most if not all 4-5 star hotels/resorts have an Internet room which is a room of computers with Internet access. Internet is usually NOT included in the hotel package and you must pay separate. Internet rooms at hotels are the most expensive access points.
In Cancun City you can find dozens of Internet Cafes. Where ever your hotel or hostel is there will be at least one Internet Cafe within a short walk. All you have to do is ask somebody at the front desk of the hotel or hostel.
Prices can change dramatically from one computer place to another. There are also Internet Laundromats, Internet Delis, Internet Pool-Halls and many small hotels and even hostels have a single computer with Internet access now.