For an interesting experince got to Korea Town for some Korean food. It is usually prepared on a grill built into the table. Gahm Mi Oak is good, as are some of the others around Herald Sq. This is a ten minute walk from Penn Station on 34th Street.

An easy cab would be to go crosstown or downtown on the west side. Both are easy sub $10 / 10 minute rides.
For crosstown try "Blue Smoke", a great resatuarant serving Southern and BBQ style grub that is excellent for a group with teens. 27th Street between Lex and Park.
For downtown try Markt, a large Belgian that will provide a great view of the Meatpacking districts nightlife.