In Tanjong Pagar, you get Korean food made by a Korean chef and be served by Korean waitresses; rare air in Singapore.
The BBQ meats you can get are all great, although it's hard to go wrong with meat. My favourite is the Sseng Galbisal (Beef short ribs) which is just un-marinated tender pieces of cow. Other dishes that I would recommend are Padak (fried chicken with spring onion) or Dak-galbi. If you get the Dak-galbi, eat 80% of it after which you should ask the staff to mix in some rice. This is a standard thing only Koreans know about and it'll leave you with some wicked fried rice to finish off your meal with.
A bottle of soju will cost around $18 to wash down the protein and private rooms are available if you need some privacy.
The ambience is more of a "let's go have a good meal with friends" type of environment more than the "i want to impress this girl".