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There are taxis at the airport. The cost will be about $US 25 up to 4 persons for the taxi to bring you to the Friusa bus station from where the express bus departs for Santo Domingo at 4 pm. Your arrival at PUJ at 2:30 leaves you very little wiggle room to acquire the express because it is about 20-30 min transit from the airport to the station and then it is best to arrive a half hour before bus departure to get a seat (first come-first serve rules), this means you have to depart (???) the airport by 3 pm. If you cannot get a seat on the 4 pm express, best to have the *taxi bring you to Higuey to the bus station in front of the Basilica to acquire a bus to Santo Domingo. The last bus leaves Higuey at 7 pm.
If that fails to get you out of the area go to the nearby Don Carlos Hotel for the night and take a early morning bus to the big city.
Regards,
PJT
*There are local buses, gua-guas, that go to Higuey from Friusa for about RD$ 60. However, they are usually crowed, have no facility to store baggage, and have no a/c.