If you plan to send packages home, it's safer to use an international courier. FedEx has an office in Santo Domingo. EPS, a local courier service, helps to offset the limitations of the regular mail service in the D.R.; though not as quick as FedEx, it's certainly better and more reliable than the regular mail.
Paid Internet access of some kind is available in almost every hotel, though you may sometimes have access to only one slow and old terminal in the lobby, maybe with a Spanish keyboard. Wi-Fi is becoming more prevalent in the better hotels even the smaller boutique properties; it's usually free but generally exists only in the lobby and some public areas, rather than in your room, but that is slowly coming. There are dozens of Internet cafés in Santo Domingo, particularly on Calle El Conde. Look up; they're generally on the second stories.
Main Post Office (Isabel la Católica, across from Parque Colón, Zona Colonial).
EPS (Calle Ortega Gaset, corner Calle Fantino Falco, Santo Domingo. 809/540-4005 or 800/200-5177).
FedEx (Av. de los Próceres, at Camino del Oeste. 809/565-3636 or 809/200-3138).
Centro de Internet (Av Independencia 201, Gazcue. 809/238-5149). Connexion Internet (Calle El Conde, corner of Calle Espaillat, Zona Colonial. 809/689-6154).