Good can-openers like Swing away--Bring two- they rust.
A standard Ecco vegetable peeler. Dominicans mostly use paring knives.
A portable cooler able to carry about 12 cans of beer.
As the others mention at, least one good kitchen knife. If you like wooden cutting boards, bring one. A small knife sharpener if possible. The climate makes knives go dull faster.
Surge protectors for computers
If you are going to want any handtools, bring them. Almost all tools are cheap from China or double the US price. A four-in-one screwdriver would be great:
A small sewing kit for buttons, etc.
Small "tap" lights with LED bulbs. At least six. Better than flashlights in a power outage for some uses. Stick one above your bed and one in the bathroom.
Condiments and spices. Montreal Steak Seasoning can be traded for a wife and a canoe in some areas. Celery Salt is cherish by "Caesar" affectionados. Pure maple syrup is also missed by some ex-pats. Black pepper in the DR is usually like dust, but Dominicans are oddly picky about salt.
I also second good soap.
An in freezer ice cream maker if you like good ice cream. Dominican ice cream is mostly air and/or expensive.