cool if ur with ur family but REALLY expensive. you can find plenty of awesome, and reasonably priced, restaurants walking around little italy. try the street vendor cannolis. they're amazing.
 if u wanna try something a little different and you like chinese food, the best dumplings in the city are in this little hole in the wall shop on the corner of Allen and Delancy st, across the street from the big chinese restaurant with the big green and blue sign. it sort of looks like a walk in place and they sell platters of four fried dumplings for a buck. we fill up there for really cheap b4 we go bar hopping.
seriously though the city is a big enough place where you will always find something cool if you just walk around enough.
basics: china town, little italy, bleaker st. for bar hopping, central park.
have fun.