The Tonight Show with Jay Leno, is indeed filmed in Burbank, CA. David Letterman is filmed in NYC Mon-Thur (Fri show is filmed on Thur also) and it is very hard to get tickets. Rachel Ray is taping her talk show here. While I live 2 doors down from the studio, I don't know about tickets. I think they start taping 9/18. Try the New York Convention & Visitors Bureau (www.nycvb.org) for that and any other shows (Try for The Daily Show with Jon Stewart - that's fun!).
I would not eat at any chain restaurant that you have back home. DO NOT go to Jeckyll and Hyde. Especially if you don't want to do the usual tourist things. The food there is awful and highly overpriced - plus they charge an extra "entertainment fee" per person. Total rip off. If you have to go - go to the "normal" one on Seventh Avenue just south of Christopher St. in Greenwich Village or to their sister location, The Slaughtered Lamb on Christopher St., though I am not a fan of that place.
To decide where to go other than the "usual" destinations, get a copy of Time Out New York or check out their website. Also try CitySearch for restaurants. You really almost can't go wrong winging it, as long as you stay away from chains and even pubs.
I do recommend Central Park if the weather is good. Get a Central Park map and go from there. Sail remote control sailboats on the boat pond or get free tickets to Shakespeare in the Park - go on a rowboat... Those are "local" things. Rent a bike and ride around Riverside Park. Take the subway to the New York (Bronx) or Brooklyn Botanical Gardens. Take the bus to City Island.
I highly recommend the Grey Line Bus Tour to get
an overview of the city - you can decide which neighborhoods you want to see more in depth from there. St. John the Divine is an excellent choice, but you still can't do the extremely awesome vertical tour (up the many stairways) since the fire a few years ago. It's the largest cathedral in North America. The Transit Museum in Brooklyn is cool. Take a walk across the Brooklyn Bridge from City Hall and go have pizza at Patsy Grimaldi's, then ice cream at the Brooklyn Ice Creamery - best view of the city. Take the water taxi back. Go to the Brooklyn Brewery for tastings and a tour.
On Saturday - go to Union Square to the Greenmarket. That's cool and fun and there's always something going on. Food wise, Zen Palate (vegetarian) is cheap and good, as is Republic Noodles, Chat & Chew and The Coffee Shop. Go to ABC Carpet & Home while you are there too - expensive but fun to check out! The wine store (near Republic) there has great free tastings (as does The Astor Place wine store). Also try Irving Place a few blocks away. Great architecture, a private park and some good food places. Pete's Tavern is a local's mainstay (as are McSorley's in the East Village and Chumley's and the White Horse Tavern in Greenwich Village - also check out the Magnolia Bakery). You are also just blocks from Washington Square Park and NYU - great sights there. Anything near West 4th Street and the East Village nearby will be reasonably priced. Go to Rocco's on Bleeker St. for the best Canoli and Italian baked goods in NY - it is the old Little Italy - pre-Mulberry St. Chinatown has cheap food. I love Lyn's Dumpling House for Chinese and Pho Viet Huong for Vietnamese (the U.N. ambassadors eat there). Chinatown Ice Creamery has unique ice cream like Almond Cookie (my favorite), Green Tea and Lychee. Look for some designer knockoff purses while you are there.
Try checking out the Chelsea Market, which is 8th Ave and 17th St. It's cool - there are good cheap eats there. The nearby Meat Packing district is expensive. There is nothing to see at the WTC site. Just a big hole. If you really want to see it, take the subway down to the World Financial Center (American Express and Merrill Lynch buildings) and go the Winter Garden, which has rows of palm trees in a giant atrium. You can look through the atrium glass for the best view of the site. Then go outside to see all the expensive boats in the marina as well as views of Jersey City, the Statue of Libery and Ellis Island. Best way to see the Statue of Liberty is to take the Staten Island Ferry for free. It is about 1 hour round trip - but an enjoyable free ride versus paying to go to Liberty Island which is boring and the statue is very hot inside.
As far as hotels, try the Holiday Inn on W 57th St. I would also check out Hotels.com - you can read the reviews at least. Rooms can be very small here. I and my family and friends who have stayed in hotels here were always here on a corporate account, so I only know: Soho Grand, Millenium Times Square, NY Hilton, Hilton Times Square, Paramount (small), Sofitel, Marriott Marquis, W on Lexington, Fitzpatrick, Crown Plaza UN, NY Helmsley, Club Quarters and the Alexander. You might want to try the DoubleTree Times Square - that looked reasonable. Also - try the Vanderbilt YMCA on East 47th St. I know it's clean and cheap.
I live here and I have always loved the view from the Empire State Building - I've been up there 3 times and am overdue to go again. If you want something different go to the Top of the Rock at Rockefeller Center. If you love crowds, go see the Today Show taping.
FAO Schwartz did reopen after the new (Japanese owner) remodeled it. The Toys R Us Times Square overshadows it now greatly.
Take the subway up to Fort Tryon Park (which is gorgeous) and go to The Cloisters (part of the Metropolitan Museum of Art) to see medieval art in a reproduction of a monastery.
Whew.... HAVE FUN!!!!