My personal compilation
OK so I've lived 1 year in Sto Domingo and ate Asian food very often. I'm leaving so let me dish it out for y'all. This is me giving back to DR1!!
My personal top is featured in this map:
Palitos Santo Domingo - Google Maps
Best Cantonese: Pan Oliva, near Hotel Embajador.
Honorable mentions: Restaurante Chino de Mariscos, on Sarasota more to the West compared to Pan Oliva. Bella Cristal (mentioned above in the thread) is not bad but the stuffy decor is not my thing.
Wok on Romulo Betancourt just West of the intersection with Nunez is a very good Fusion chinese restaurant. The edamame dumplings are awesome as appetizers. The food is plentiful.
Best Shanghainese: Expreso Yu in Naco/Piantini (on the map above).
There's another tiny one called Shanghai express (?) on Romulo Betancourt just west of Wok on the same side of Romulo Betancourt, but it's not as well stocked and especially is low on vegetables
Best Northern cuisine: the one near INTEC on the map above. The place looks like your average pica pollo student cafeteria but the guy is the former cook to the embassador of China and the food is awesome--the Chinese food at least--I mean, I have not tried the fried chicken that stands for "Chinese food"!!
There are plenty of very, very nice Taiwanese vegetarian cafes where I had many meals. Their meat substitutes are tasty and... the food is incredibly cheap.
Manna and Jardines Seul are excellent Korean restaurants in Bella Vista.
If you like Szechuan food you're out of luck--I don't know any place in town that has this kind of spicy.
There are some Chinese restaurants in and around the "Chinatown" portion of Av. Duarte but nothing that I remember as exceptional.
There's a Pakistani lady that cooks some South Asian food (on map with phone number). Like a taxicab hangout place in New York, but outdoorsey. Only lunch.
The only Vietnamese place that I know of is Riz Dor? in Las Terrenas--not in Sto Domingo!!
I don't count the number of sushi places. I think the "aplatanado" chains like Sushiya and Yokomo are just fine. Samurai in Piantini has better decor but the menu is not that diverse (aside from their tasting menu), many items are too salty and it can be way expensive.
To buy food items the best place is the Asiatico mini-supermarket on 27th of Feb -- can't remember if it's close to Nunez, Privada or Caonabo. It's near the NW corner of one of these three intersections though.
Finally this blog is in Japanese but just going by the pictures and phone numbers and you can discover great places:
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Enjoy!