Check the hours of museums, but some of them are too big to be seen in just an hour. Most of the IMAX movies sell out early in the day, but you might be able to buy tickets over the internet.
MIDTOWN:
Visit the original Pooh Bear and his friends at the NY Public Library:
http://www.nypl.org/events/exhibition/2009/05/31/winnie-pooh-and-friends-original-toys
If they liked "Between the Lions," the first Ghostbusters movie or the Percy Jackson movie, visit the Lions outside the the main branch of the Library.
NBC has Studio Tours and Radio City Music Hall does backstage tours, but you need reservations.
Check their sites for times; I think they went until 6pm, but that might have been during the holiday season.
Go ice skating in Central Park (Wollman or Lasker rink) or Rockefeller Center. I think the Bryant Park skating rink is closed for the season now.
The kids probably won't be impressed, but there's an underground shopping/dining mecca beneath 6th Avenue from 47th street to 52nd street.
It's a neat place to explore - the kids always think we're going on the subway, but we walk through the art deco halls and look at all the windows.
You could ride the subway into Brooklyn and back on a train that crosses the Manhattan Bridge. The view is awesome and the kids can wave to the drivers stuck in traffic, lol.
FAO Schwartz is a famous toy store that has a lot of cool toys and things to see/try. It's the store from "Big" with Tom Hanks, where he plays the floor piano with the toy company magnate.
Go to Times Square after dark to check out the marquees, signs and lights. You could go see a movie there or the TKTS outlets sell same-day theater tickets for half-price, that might make it affordable for you. Some theaters have "Student Rush" tickets for cheap as well if the kids have IDs.
The Percy Jackson books and movies describe many sites and landmarks in Manhattan, so you could go see those things with a checklist.
DOWNTOWN:
Go to Chinatown and buy a paper kite or a pair of chopsticks. The food is pretty cheap, too. (Wo Hop - 17 Mott Street - Downstairs!) Play a game of tic-tac-toe against the chicken in the arcade on Mott Street. (The best you can hope for is a draw since the bird always gets to go first, lol.)
Walk over towards the South Street Seaport and look at 127 John Street for a few minutes after dark - they have lights on the building that are fun to watch.
Downtown Manhattan does get pretty empty and many places close after 6-7pm, but they don't roll up the sidewalks, as someone implied, lol. One game I used to play with my kids was "Eye Spy." The tops of many buildings in downtown have spires and statues that make the game interesting. "I spy someone with scales." After they can't find a fish, you can teach about Justice's scales on top of City Hall.
Whether or not you want to visit Ground Zero is up to you. The buildings are progressing, but to kids, it's just a construction site at this point, unless the museum's open already. (Not sure - check with your hotel concierge.)
Take a round-trip ride on the Staten Island Ferry - Lady Liberty is awesome after dark and the bridges are all lit up with their necklace lights.
Right next to the Ferry on the SI side is the Yankee's minor league stadium. Tickets are pretty cheap, if there's a night game. There are bars and restaurants in St. George (where the ferry docks) but they're not particularly kid-friendly.
If you're up to a long (45m each way) subway ride, take the train to Brooklyn's Coney Island and ride the famous Cyclone coaster and Wonder Wheel. It will make them appreciate Disney theme parks, but it's still a thrill. Unfortunately, the Carousel with the rings to catch is closed now and the Steeplechase is long-gone.
The Mets minor-league team has a beautiful stadium in Coney Island called the "Cyclones," but with the travel time, you won't have enough time to watch a game and get back to your bus, so probably not an option. Still, it's a nice stadium to see.