The hot clubs are dispersed around town, as there is no real downtown in Santo Domingo. So taking a taxi is a must - they are however all within proximity to each other, and taxis are cheap.
Places you might want to check out.
Dock - for drinks at Acropolis Center
Le Suite - Across from Plaza Central
LED - Hotel Hispaniola
Amika - Off Lincoln Ave
Nubar - Cant remember exact location
Cinema Cafe - Plaze de la culturar (live music venue)
Atarazana 9 - Colonial Zone
Theres a few other places people mention, Beat, Tonic, Retro, Zin, Pravda, Praia, Segafredo, Hard Rock Cafe, Tangerine. For more Salsa, Merengue, Bachata, there's Jet Set (ave Independencia) Montecristo (lincoln) and several others, I'm sure someone will mention the clubs on Ave Venezuela in the east end.
Strip clubs - Doll House on the Malecon, its the most reputable.