This is what I like to do with out of town tween girls in NYC. Here is the secret to being a great tour guide. Keep them fed at frequent intervals. Don't walk them like a regular New Yorkers; they will turn zombie on you. Jump in a cab FAST when you see it coming on. Keep the destinations varied; educational, silly, glamorous. It is hard not to make a tween trip all about the shopping, but if you sprinkle a little interesting and inexpensive shopping in between the museums, they may stay alert.
Upper East Side: If you are doing a museum (and you are taking your life in your hands to do two in a day) head further east and take a ride on the Roosevelt Island tram. Pack a deli sandwich to eat on Roosevelt Island, take a breath and look at Manhattan, stop in at Serendipity if there is no line (ha!) for a frozen hot chocolate, and top it off with a little shopping at Dylan's Candy Bar. Even though I am tired of it, Dylan's may just be the highlight of their trip.
Midtown: You could stop in at the Toys R Us to wait in line for the Ferris Wheel, but we like to ride the elevators in the Marriott Marquis for free (did I mention that they are glass elevators?). Get an "outside" elevator, one sort of in the center, ride all the way to the top floor and try for an uninterrupted trip to the ground floor. Repeat until you stop squealing. Then head across the street to the Edison Hotel restaurant for matzah ball soup, blintzes and egg creams. We also like to use the bathrooms at the Paramount or whatever fancy new boutique hotel has just been renovated. Undoubtedly, they have a Sephora at the mall at home, but you want to be glamorous when you go to Broadway. We go for makeovers before the show and put on the most fabulously outrageous peacock colored eyeshadow imaginable. It doesn't fly back home, but heh, you are having a madcap Manhattan weekend. The best lunch or dinner spot ever is the Burger Bar in the Parker Meridian in midtown. You go into this sleek, grand lobby, look for the small neon burger sign and enter another world; cardboard signs, grease stained paper bags of french fries and the occasional celebrity. The burgers aren't only great, they are the best bargain in town. You can't miss.
High tea is fun for tweens. Although I like to wear a big flowered hat, they usually don't allow it. It is great to stop for a fancy version at the Palace or some other institution, and contrast it with Tea and Sympathy in the village. There are some pretty good walking tours in the village as well. It is interesting for them to see a real speakeasy at Chumley's (even if it is only from the outside), the skinniest house, see the site of the Triangle Shirtwaist fire (which they study about in school) and the bodies buried under Washington Square Park when it was considered way out of town. You have to go to The Forbes Museum on lower 5th Ave. It is free and it is the perfect tween collection of Faberge' Eggs and Toys, beautifully displayed (I think that it closes at around 4 so don't leave it to the end of the day).
I like Sundays downtown. Dim sum at some huge Chinatown dumpling palace will blow their minds. Shopping at Pearl River, and a scoop of red bean or green tea at the Ice Cream Factory is always a hit. Then a tour at the Tenement Museum and a pickle on the lower east side. As long as you are downtown, walk across The Bridge and have some cheese cake at Juniors. Sit at the counter for the most colorful waiters.
I don't like waiting in line for things; it wastes time and drains energy. For me the Staten Island Ferry is a great view of the Statue of Liberty. The Empire State Building is open until midnight, so if you go early evening your wait isn't horrible (if you go at 11pm, it is even quieter, but there are lots of people kissing)
The best tour for out of town relatives that I ever heard was mentioned on WNYC. You get each visitor to write a country name on a slip of paper. You proceed to eat at a restaurant from each of those countries during their stay. You wake your guests at midnight, hop in a car and drive to Time Square to demonstrate that this is in fact, the city that never sleeps.