In Santo Domingo you would definitely find all that type of stuff in Duarte, north of the Colonial Zone and Chinatown, running into Villa Consuelo. This area has an amazing selection of fabrics and everything to go with them. It is quite a rough area, so I would strongly recommend going with a Dominican, dress like a local (i.e. long trousers, not beachwear) and don't carry anything which could easily be snatched. I love mooching around this area though and I've bought some amazing fabrics there.
Option 2 if you want something more civilised is the store called El Canal in Luperon, again they have a huge fabric department and I am pretty sure they will sell everything you need to make quilts.