September is a fine time to visit NYC.
Since you'll be there for a week, you'll have plenty of time to devote a day or two to the outer boroughs, where there's some interesting eating to be done.
I would recommend a visit to the Bronx Zoo and the NY Botanical Gardens, both of which are in close proximity to NY's real Little Italy, Arthur Avenue.
Queens has some amazing ethnic eating experiences available at a fraction of the cost of what Manhattan dining will cost.
Go to Brooklyn and visit DiFara's, where pizza is presented in its highest form, or out to Coney Island to Totonno's.
I think tourists miss out on a lot of the flavor of NYC when they ignore the outer boroughs. Don't be one of them. There's plenty to do and see in Manhattan, and it would take a lifetime to take it all in, but the other boroughs have much to offer as well.
For dining research, this is a pretty good site:
http://www.seriouseats.com/newyork/Also, since the names of neighborhoods can be confusing to visitors, this simplified map will give you an idea of where things are relative to one another:
http://images.google.com/imgres?imgurl= ... image&cd=2Don't get sucked into Midtown - the best eating is south of where you're staying.
"I say: find cheap wines you like, and never underestimate their considerable charms." - David Rosengarten, "Taste"