Local buses are called gua-guas, and although not pretty or classy, they'll get you where you're going—not necessarily quickly, but certainly cheaply. You'll marvel at what people bring on the bus; we've seen a musician's kettle drum, Haitian paintings, or a 25-pound sack of rice. From Playa Juan Dolio near Plaza Oasis, you'll pay about RD$30 to go to San Pedro de Macoris, RD$65-RD$80 to La Romana, and RD$80 for Santo Domingo (be sure to take the express). You'll pay extra for luggage. Though crowded and frenetic, using a gua-gua is doable, and since the typical taxi fare is $50 for an hour trip, the gua-gua will be much easier on your wallet.
Motoconchos (motorcycle taxis) are usually found at the gua-gua stops. Ride at your own risk.
If you're staying at a hotel, you can arrange a taxi there. If you're an independent traveler, there are a couple of recommendable companies you can call. And if you find a driver you like, get his cell number so you can call him directly.
Juan Dolio Taxi (Playa Juan Dolio. 809/526-2227). Santa Rosa Taxi (La Romana. 809/556-5313).