Not sure how long you're going for, but below should keep you going for a couple of days (we walked a lot but you can always get a subway for a bit if you want, but it's a fantastic city to walk around in).
I lived there for a few years in the early 90s but never really went to many of the tourist spots, went back last year with wife and kids and really enjoyed it.
Day 1.
Walk down 6th Ave to Rockefeller centre, you will go past Radio City Music Hall.
Go to Top of the Rock Observation deck, earlier the better as it gets busy.
Walk to Bryant Park, sit and get a bite to eat from "Waffles and Dinges".
New York Public Library is right beside it if you want to take a look.
Keep walking and at 34th Street you will pass near Empire State Building.
Veer left onto Broadway and continue to Madison Square Park, this is right beside the Flatiron building.
Take 5th Ave down to Washington Square Park for a look around - always something going on there.
McSorleys is nearby if you want to visit for a pint, they only serve their own ale, and it's cash only.
After that head west over to Bleecker Street for some proper NY pizza, Johns's of Bleecker St is one of the most famous but there are others too.
You can walk past the Blue Note Jazz club on the way.
Nearby is the Friends Apartment building if your daughter wants a look.
Walk from Friends Bulding west to Washington Street, then north for a few blocks and that brings you to the High Line.
You can walk along the High Line north to Hudson Yards.
Day 2
Subway down to Brookly Bridge, walk across the bridge - do it in morning before it gets too crowded.
Time Out Market for breakfast.
Walk over to Dumbo for famous Manhattan Bridge view/photos.
Parks near the water have great views back to Manhattan too.
Get East River Ferry back across to Pier 11 and it's a short walk to Wall Street.
Walk over to Battery Park for a look around and you can get the ferry from there to Ellis Island.
I wouldn't bother getting off for Statue of Liberty, you will go right past it anyway.
When you come back the World Trade Centre and 911 Memorial are only 10 mins walk.
Baseball game in the evening well worth a go - either the Mets or Yankees stadiums are easy to get to.
