No you don't pre register - you wait on line early in the morning. VERY EARLY depending on who the guest is. IE if it is a day Justin Bieber is there, ay yay yay.
Depends on what you and your family like to do. There is Canal Street, Chinatown where you can buy knock off handbags. There's little Italy. There's the South Street Seaport and ground zero. These are all downtown Manhattan type of things.
Uptown Manhattan you have the Cloisters, you have Central Park. You can rent boats there relatively inexpensively and row on the lake for an hour, and eat at the boathouse.
You can go to the Museum of Natural History, the Met, MoMa, the Guggenheim. Are you museum people?
Top of the Rock is cool. You can also tour NBC studios. There's the Statue of Liberty (has to be booked in advance).
There's the Staten Island Ferry which is free and a nice ride.
There's the Coney Island boardwalk but now you're out of the city and into Brooklyn.
And on and on.
It depends on your likes and interests and your kids likes and interests and your budget.
If you love Italian food, I highly recommend eating at Carmines. It is "touristy" but awesome and fun.
I would see a broadway show.
You can also go do trapeze over by the river. I forget the website for it.
PM me if you want, and give me more of an idea of things you're into and ages of your kids, and I would suggest some top things.