Yes, definitely rum! Not a lot of people drink tequilla in the DR! Tequilla is a Mexican drink.
Lots of people drink rum with just ice, and many mix it with refresco - soft drink, such as Pepsi or 7 UP. The "best" is Extra Viejo rum, but "Anejo" has teh best taste when mixed with soft drinks.
Rum & Coke is called Cuba Libre.
Pina Colada with alcohol also includes rum.
There are also other rum cocktails, but you usually get them at resorts or high end bars. The regular dominican rum fare is rum + ice + soda.