You can try this cafe situated at Korean Cultural centre, which is basically it's canteen.
Korean Culture Centre in Lajpat Nagar nearest to Moolchand metro station
Gung The Palace is a great option. However you can even try Sakura Arigato!
Safdarjang side there are a lot of restaurants also if you want Korean noodles or anything you can go to INA MARKET
Gangnam Korean in majnu ka tilla
Try majnu ka tilla they have variety of cafes