Don't do anything you wouldn't do at home.
Moving around late at night without "backup" especially for foreigners can be risky.
Cheap is not always best. There is security in a good door with a good lock in an establish hotel that employs security personnel.
Always remember where you are. The Dominican Republic is a high end third world country. Officialdom is rife with corruption, your embassy will be of little help in a personal crisis. Don't travel here without good medical insurance and a way to get yourself evacuated home for treatment if need be.
Have lots of money available to you should you need it but don't carry a lot of money on your person at any given time.
Leave jewelry and expensive cellphones, computer tablets at home.
Be wary of those who approach you unsolicited offering to help you do things, find things, resolve issues.
Have a good communication plan in place. It is imperative that someone always knows where you are, what you are doing, how & when you are travelling between different places in this country. These people should know who to contact if you miss checking in at predefined times.
DO BRING your common sense and encourage your inner voice to speak up whenever something seems too good to be true, too convenient or a bit surreal and potentially dangerous (couch surfing falls into this last category).
Have a good trip.