The Internet is widely available in the Dominican Republic, though even in the capital Internet cafes are not as common as in other parts of Latin America . As an expat you will probably want to think about getting a connection set up in your home.
Santo Domingo offers the widest range of options for getting connected outside your home. Internet cafes will charge between RD$35 and RD$70 an hour (plus more for printing, burning CDs etc.). You will also find that most of these shops double as call centres where it might be cheaper to phone internationally than on your mobile.
WiFi can be found all over the capital with many American fast food chains offering free access. The Acropolis Mall also offers WiFi throughout. Elsewhere in the country, it’s harder to find - though many resort hotels offer access for a (hefty) fee.
As with mobiles, Claro, Orange and Tricom are the big players when it comes to home Internet. Most offer you a choice of ADSL or cable connection. If you can, go with the former which will be faster and more reliable. You might also consider getting a dongle where you pay for usage over and above your monthly data limits, although this is currently only available from Orange. It’s also worth bearing in mind that Claro offer a rural broadband package (banda ancha rural) which could be useful if you plan to live somewhere more remote.
Whoever you decide to go with, make sure you read about the different packages carefully (there are a bewildering array of these). You can sign up for a combined package of TV, internet and phone with Claro or Tricom.
Choosing a monthly mobile package from any of the main providers will probably get you get a certain amount of mobile data included. If your phone is enabled with 3G from your home country, you may be able to access Internet on your mobile in the Dominican Republic, but beware the often extortionate data roaming charges! A pay-as-you-go SIM from any of the major networks should also enable you to get online, providing your phone has Internet capabilities.