As a native New Yorker who grew up in Manhattan, I would advise that you give Brooklyn at least as much time as you do Manhattan. Yes the Met, the Whitney, the Guggenheim, and the Chelsea galleries are in Manhattan, but the cultural heart of the city is on the other side of the river now. The music scene and many of the better music clubs are in Brooklyn. And while there are fantastic restaurants in Manhattan, many of the more exciting (and more affordable!) ones that are opening these days are in Brooklyn. Some Brooklyn neighborhoods to visit include Fort Greene, Williamsburg, Greenpoint, Cobble Hill, Carroll Gardens, and Park Slope. I wouldn't advise going to Ground Zero. It's just a giant construction site. It's from a distance that you get a much better sense of what we lost. Take a walk across the Brooklyn Bridge and stop at the viewing area and take a look at the lower Manhattan skyline and try to imagine the two absent giant towers (and all the people who were inside).
I Just noticed that you may or may not be staying over night. Hmm, in one day I wouldn't be too ambitious. There's too much to see and do. You could spend six months here and still not get around to everything. Just go see that luthiers exhibit and have a walk in Central Park. If you do decide to spend the night though, I think you'll be able to find something affordable if you look around. I got married last summer and many of our out of town guests were able to find rooms for $150 a night I'd recommend not staying in Times Square. It's very touristy and unpleasant. . Another option, and one people don't generally associate with New York City, is to stay in a B&B. Anyway, have fun.
Oh, and how could I forget. Here's a quick rundown of some of the guitar shops:
Rudy's on 48th Street is pretty much the only decent guitar shop left on what used to be guitar row. The only other shop on 48th is Sam Ash. Rudy's has another shop in Soho too. Near Rudy's Soho shop is Matt Umanov, which has a great collection of vintage guitars, particularly acoustics. Around the corner from Umanov's is Carmine Street Guitars, which is a very small shop, but sometimes has some interesting stuff. Southside Guitars in Williamsburg, Brooklyn is a medium size store that tends to carry more Guilds than the other stores around town. Not too far from Southside is Main Drag Music. Besides cheap-o parlors -- Silvertones and such -- Main Drag doiesn't have much of an acoustic collection, but they lots of cool amps and electrics. All of the above shops have websites, so you can look them up beforehand and see what interests you.