You will probably get more up to date suggestions from people actually living in and around Santo Domingo.
Yet, I remember a place on Westbound 27 de Febrero next to the BON ice cream parlor and above Richie Music which advertised teaching people how to dance Salsa in 21 Hrs. At least that was 4 years ago... I don't know if it's still there but the phone number was 809-622 2020.
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I think that a beginner to dancing should consider approaching Bachata first. It uses virtually the basic steps of Salsa but at a much slower pace so one can experience some success quite quickly (1, 2, 3, pause, 1, 2, 3,...) You will want to take at least a few lessons with somebody who REALLY knows how to dance correctly and how to teach it. It is my opinion that, while most Dominicans think very highly of their blood inherited dancing skills, most actually don't perform much which would make enough sense so it could be taught. That may be "OK" to get by with if you grow up with that music and the rhythms, but for somebody new to dancing, the culture the rhythms and the moves... it's hard to get into without proper understanding of replicable patterns.
Oh, one other thing, learn to listen to the bass more than to all the percussions. It's a more reliable indicator of where the beginning and the end is and it will help you quit thinking in 1, 2, 3's and thus enjoy more the music and dance.
... J-D.