You can get half-price tickets at the TKTS booth, but you can also get regular-priced tickets by waiting on line at each theater's box office early in the day. They sometimes have left-over seats, usually in the mezzanine, for the matinée that day.
You've got a lot of good things planned! However, I think you'll have trouble with some of it. As others have said, it's going to be very hard to get tickets to the Lion King, Wicked, and Mary Poppins on the day of the show. It'll also be hard to get tickets to Grey Gardens after all of the Tony nominations and wins (same is true of Spring Awakening), and The Little Mermaid doesn't open until December. Rent shouldn't be a problem, but I wouldn't count on the others. Hairspray and Mama Mia are good alternatives. There are also a lot of great Off-Broadway shows to see, like Forbidden Broadway: SVU, Altar Boyz, and The Great American Trailer Park Musical.
When it comes to the Museum of Natural History, you HAVE to go early. If you do happen to get Lion King tickets I wouldn't plan on going to the museum afterwards. The Lion King matinee is from 2:00-4:00, and it could take a good half-hour to get over to the museum afterwards. The place is HUGE and there's a ton of amazing things to see. It's been my favorite museum since I was really young. It really is a magical and awe-inspiring place. Don't miss the ecological exhibits (the animals and fish from around the world in displays that look just like their natural habitat... including the famous giant blue whale!), the huge dinosaur exhibit which takes up the entire top floor, the BEAUTIFUL Hall of Planet Earth that is full of glowing gems and minerals, and the controversial yet completely fascinating evolution exhibit. The museum's one of my absolute favorite places in the world, but unfortunately it closes at 5:45, so you really won't have time to see or do anything. I would make a day of it and get there as early as possible, and then walk around Central Park afterwards. At night they also have a really amazing laser rock show at the Hayden Planetarium. It's only on select Friday and Saturday nights so you'll have to check to see if it's showing. The music isn't very loud so you shouldn't have a problem there, and sitting back in the reclining seats in the middle of a HUGE dome-shaped theater while you watch the lasers and special effects synced perfectly to the music is literally INCREDIBLE! It's one of my favorite things to do.
When it comes to other stuff to do, the Top of the Rock is a great alternative to the Empire State Building. It's cheaper and provides an amazing view of the Empire State Building, itself. The whole experience is set up in a really cool way, and it has the most fun and unique elevator ride ever! In the same building is the NBC Experience Tour. My dad works at NBC so we've never done the actual tour, but it's a lot of fun and really exciting just to be in the building. You may even run into Conan or one of his guests!
There's also the Sony Wonder Technology Lab on 56th St. and Madison Ave. It's like a big DisneyQuest but themed towards the Sony technology of today and tomorrow. Everything is hands on and a ton of fun, and best of all, it's completely free! There are games, experiments, picture-taking opportunities, simulators, etc.
As someone else has said, regardless of how many times you've been to the city, I can't see anyone ever getting bored. There's a million and one things to do, and there's always something new. If you've already been here 4 times I would skip the double-decker bus tour, it's really just a tourist trap. They only drive you around to a few sites in Times Square, which are all a lot easier and a lot more fun to see on your own instead of from a bus. If you're looking for something unique to do, how about Chelsea Piers on the lower west side? They have a ton of different activities including batting cages, a bowling alley, soccer and baseball fields, basketball courts and year-long indoor ice skating. A few blocks down is the famous Trapeze School which is amazing in and of itself! I'm not sure if your group is into stuff like that, but if anyone is extra adventurous it's definitely a fun experience! Have you been to the Statue of Liberty and Ellis Island yet? That's always a really nice day out. For a special night I would also book a cruise through Spirit Cruises. We go every summer as part of an NBC employee party and it's an amazing night out. The dinner cruise includes either a sit-down or buffet dinner, along with a live band for lots of dancing and a fun, family-friendly atmosphere. The view of the statue of liberty and the city skyline first glistening in the sunset and then all lit up at night can't be beat. If you're still looking for more fun stuff to do, Madame Tussaud's in Times Square is one of my favorite places. You can take the best, craziest and most absolutely HYSTERICAL pictures in there since you can touch all of the wax figures!
They also just recently opened a new Ripley's Believe It Or Not Odditorium in Times Square. We haven't been there yet, but we've been to the ones in Atlantic City and Orlando and are always fascinated by what they have on display.
And don't miss the
Disney Store on 5th Ave (they even have character meet and greets!), the giant indoor ferris wheel at Toys R Us Times Square, and the new M&M's Experience Store. It's huge!
If you don't mind venturing out of Manhattan, the Bronx Zoo is continuously ranked the top zoo in the nation. It's the largest metropolitan zoo, and is located in the Bronx, only 20-minutes outside of Manhattan. If you're renting a car it's a quick drive, or there's a special bus that takes you right to the front gates from Times Square. The zoo itself is humongous with a ton of incredible exhibits that perfectly replicate the animal's natural habitats. The Congo exhibit (home of the Gorillas) is the most amazing animal exhibit I've ever seen. It's the closest you'll get to Africa without leaving the country!
When it comes to food, you've already got a great one on your list - Ellen's! Sure it's a novelty restaurant, but the food is AMAZING and it's one of our very favorite restaurants. It's also cool that all of the waiters and waitresses are either on or were on Broadway and they all sing as they deliver the food and walk around the restaurant. It's a ton of fun. If you're looking for good Italian food, definitely try Daniela's Trattoria. It's on 8th Ave between 45th and 46th streets so it's right in the middle of everything, and it's the best Italian you'll ever have. We're regulars there! Also try Bubby's Pie Company in Tribeca. It's down-home cooking (southern/comfort foods - mac and cheese, pulled pork, fried chicken, fried okra, hush puppies, etc.) in a really cute restaurant in one of the best neighborhoods in the city.
Let me know if you have any questions, I've got TONS of suggestions!
