If you are looking for a great supply of (not just Chinese) Asian ingredients (Thai eggplant to frozen kaffir lime) and supplies (from mortar-pestles to bamboo rice steamers) you will not be disappointed (after braving through the gates). If you want to have Indonesian spices and goodies, come to Topline. You also can get Thai, Philipino, and other exotic SE Asian condiments and ready-to-eat snacks.
All the ingredients you will ever need for Malaysian, Thai and Vietnamese cooking can be found here. Here, you can find Pandan Leaves, Belachan, Lime Leaves, Gula Melaka, a whole host of spices, and whatever else tickles your fancy. They are right in saying that they're an Indonesian, Thai, Asia Market etc. because everything that you ever want from South East Asia is right here.
One of the largest and probably most well known-popular super markets in Chinatown. They have an awesome selection of sauces and pastes you get from Asia and a great selection of Asian snacks! Hands down, best Chinese grocery store in Manhattan. They even have a basement with miscellaneous goods like cooking equipment, utensils, household items, etc
This is one of the best Asian supermarkets in all of NYC. They have high volume sales so everything is fresh. The cashiers are nice and fast. A lot of excellent selections on Asian vegetables, snacks, frozen foods, sauces, noodles, drinks, and a great butcher and fresh seafood section. They sell Thai, Filipino, Japanese, Korean, products aside from Chinese for years. It has a parking lot for customers at the back and a coffee shop too.