Don't get a rental car! The subway will take you everywhere you need to go. It looks pretty confusing at first but is actually pretty easy. People are willing to help. During game days just follow the jerseys! Stubhub or ebay are the best.
Last year for both Yankees and Mets stadiums. Little Italy and China town are right next to each other. You can pretty much get fake bags anywhere now. According to my wife the best ones (actual real ones tht "fell off the back of a truck) are down by the Statue of Liberty. Everytime we go into the city she comes back with two more purses. Get a watch for yourself!
Someone mentioned the Rockefeller square. You can do a tour of NBC studios, you can see the following sets:
Studio 1A - Home of Today Show
Studio 3A - Home of Dateline
Studio 3C - Home of NBC Nightly News
Studio 6A - Home of Late Night with Conan O'Brien
Studio 8G - Home of Football Night in America Studio
8H - Home of Saturday Night Live
ShopNBC.com - NBC Studio Tour
Plus is is right by radio city music hall and other great sites.
Statue of Liberty/ Wallstreet & twin towers are right next to each other (easily walkable)
Madison Sq Garden/ Times Square/ Rockafeller/ & Central Park are close to each other as well.
My advice is don't plan too much, leave some time just for walking and seeing the city. Every corner has something else to see. TONS of things to do and see.