I lived there all my life until moving away five years ago, and I was a pizza addict while I was there, so I can tell you from first-hand experience that you're gonna enjoy the pizza
Let me start by saying that asking what's the "best pizza" in Manhattan is a loaded question. If you ask 100 New Yorkers that question, you'll get 100 answers. That being said.......
There's some threads in the "Restaurant Reviews" section about NY pizzerias...you might want to have a look there. You might also want to have a quick look at sliceny.com, which is a website dedicated to NY pizza, and a great resource.
As I think I said in one of the aforementioned threads, there's two sides to sampling NY pizza--you have to go to one or more of the "elite" pizzerias: Lombardi's, John's, Grimaldi's, etc. Then there's the myriad "street" pizzerias that dominate the NY landscape.
Some of it depends on how far you want to go, depending on where you're going to be in Manhattan.
For me, of the elite pizzerias, I happen to prefer Lombardi's, the first pizzeria in the US. However, others will disagree with me...and maybe they're right, since I've heard tell that L's pizza quality isn't what it used to be. However, for the history alone, and the location (right in Little Italy), I don't think you can go wrong with a Lombardi's trip. Grimaldi's is in Brooklyn, so if you want only Manhattan pizza, that's out. Lots of folks on this board have recently been trying to duplicate Patsy's pizza...there's plenty of pics in those threads, check them out.
As far as "street pizzerias" go, my personal favourite has always been Ben's Pizza on W. 3rd Street and MacDougal St. (a block away from the W. 4th St. subway station and Washington Square Park). I lived there, so maybe I'm biased, but I always liked them more than any other pizzeria in the neighbourhood. I also liked Stromboli Pizza just south of Union Square, next to the University Bowlmor bowling alley. There's also a version of "Joe's Pizza" on Sixth Avenue and Carmine St., owned by the famous Giuseppe Vitale who owned the original Joe's Pizza that closed recently, which was considered one of the best street pizzerias in NY. However, having lived there and eaten there for years, I can tell you I was more impressed personally by Ben's than either Joe's outlet.
Of course, there's always the infinity of Ray's Pizzas, including the famous one on Sixth Avenue and 11th Street that everyone mistakenly thinks is the real "original Ray's." I ate there a couple of times, never was all that impressed, and thought there was way too much cheese. Of course, my last time there was 10 years ago, so it's quite possible it's changed.
To be honest, other than Lombardi's, I always preferred the street pizza to any other brick/wood/coal oven elite pizzeria. Ben's was a lot cheaper, a lot quicker, and a lot tastier than any other place I went to. But that's just my personal preference.
My best advice: depending on where you're going to be staying, grab a yellow pages or a concierge and find out where some pizzerias are in your immediate area....then do a walking tour!
Good luck, and report back when you return!