I went to Mexico in March with my daughter, and silly me, I left my laptop at home and decided to just use my phone. I ended up with a bigger bill than I wanted, even though I kept my use to a minimum. The place we stayed did have internet, so I could've checked in over that instead, and could have Skyped instead of called on my phone... Next time!
The place we stayed had an Internet Cafe where for very little cost you could use their computers.
If you have a Smartphone, you can set it up to use the wifi connection when you are at your resort, so that will cut down on your data usage some.