Doctors Cave Beach Hotel in Montego Bay has internet but i`m not sure is free, also Gloustershire Hotel , Emerald View Resort Villa located at 12 miles from the airport is a reasonable place to stay and has complimentary dial-up Internet access.
Hope my answer has been helfpul!
Try using the "build your trip" flight comparsion tool here:
Flights To Jamaica it will
search multiple websites and get you the best price.
Links of interest:
Montego Bay Hotels Things to Do in Jamaica