The official language in Dominican Republic is Spanish and although a lot of people in hotels speak English it is not a bad idea to learn some Spanish. Most likely if you are coming to Punta Cana you will not be that interested in learning, but if you decide to stay longer there are number of language schools in the Dominican Republic. Good places to learn are either the capital Santo Domingo or Cabarete.
If you intend on learning Spanish in Punta Cana your best bet would be finding a private teacher. They will probably charge something like US$25 for an hour for private lesson.
These are some private language schools in the Dominican Republic teaching Spanish: