Don't know how old your "kids" are, but if they are young, they could get trampled, separated, frightened, etc. Crowds are HUGE at New Year's. I wouldn't bring them down there any time after the street closes to auto traffic, which is about 6PM.
If you are talking about teens, be aware that they have to be WITH you at all times. Curfew on NYE is from 6 PM December 31st to 5 AM on January 1st. The police have no "wiggle room" on this at all (so don't even let your kids go browse a souvenir stand or go to the bathroom without you). You should read
this, which explains in more detail about children, teens, and curfew on NYE.
Fern