I was born, bred, and currently reside in NYC.
Traveling the subway system with a wheelchair is difficult, but not impossible. It's important that you plan your ride because not all stations have an elevator. The Lexington avenue line (east side) station at 125th St. does have an elevator (I'm not sure about the west side), and most major stations (like Grand Central, Times Square) have elevators.
Definitely avoid rush hour (7am - 10am, 4:30pm - 7pm) on weeekdays.
All City buses accomodate passengers with wheel chairs, but rush hour difficulties still apply.
The following link provides all the info you'll need about trains/buses.
Cabs are an option, but can be pricey when you are unfamiliar with the city.
I hope this helps. If you have any other questions, let me know.
PS If you're going to the Village, do not purchase marijuana in Washington Square Park - it's very low quality, if it's marijuana at all.