Don't stay in Times Square. You'll... be in Times Square. It's just a disaster.
The Beacon is nice, it's on 74th and B'way though - two blocks from the train, which is one stop from Times Square. There's also the On The Ave. hotel in that same area, the Library Hotel is very nice, there are a bunch of nice hotels down in SoHo to check out...that's an awesome neighbourhood, great to walk around (as is the Upper West Side, where the Beacon and On The Ave. are), shopping, restaurants, and Times Square is really accessible from everyplace - you just don't want to spend any time there. You want to get in and get back out.
Especially, especially, stay away from the Marriott in Times Square, it's a death trap, someone is always getting killed or mysteriously flying out of the windows of that sucker. It's a trashy mess.
As for shows - if there's something specific she wants to see, book now. If she just wants to see some shows - go the TKTS route, it's fun. They can take the train down to John St. (Do not go to the TKTS booth in Times Square) in the afternoons and pick up tickets from whatever's available at the booth for that day for like half price.
As for travelling, always fly into Laguardia, it's closest and simplest. DO NOT rent a car.
To get here from the airport you can take a cab (not too expensive from LGA) or the big blue shuttle and to get around the city, you can take the train, buses and cabs. Don't limit yourself - train is fastest.
Also, plan some out-of-the-way stuff. See Columbia University, take the Staten Island ferry, tour the Tenement Museum, go see what's at BAM, etc.
For tourist stuff to do - the MET, do go to Central Park, do go to the Empire State Bldg. (as late at night as possible, they're open nice and late), Wollman Rink, you can eat at Serendipity's, heh.
Stay away from - Statue of Liberty, WTC (unless it specifically means something to you), Rock Center (unless you just go at like midnight to peek at the tree, do not attempt to skate there), etc.