Transportation
Taxi
Accessible Dispatch is a service in New York city you can use to get an accessible cab anytime. You are charged the standard metered rate. You can request a pickup anywhere in Manhattan to a destination anywhere in the five boroughs. You can make your request via phone, text, online or smartphone app.
http://www.accessibledispatch.com/
Subways and Buses
You can purchase a MTA 7-day pass for $30USD. Purchases can be made at subway station booths with cash, at vending machines which are in all subway stations with cash or credit or debit cards, or at many local stores. Buses accept exact change or MetroCard. Customers with visual impairments may use an audio feature that will prompt them through the use of the vending machines. Take note that if you're going to pay the cash fair on the bus they do not take paper money, coins only. I found this odd considering the US doesn't have $1 or $2 coins.
The New York subway as of 2012 has 97 ADA-acessible stations. The listing of them can be found here. http://web.mta.info/accessibility/stations.htm You can also find the status of the elevators on here at this website http://advisory.mtanyct.info/EEoutage/
Food & Drink
New York is an expensive city no one is going to debate that too much. Here are a few cheap eat guides I think look decent that should help you find good food on a budget.
http://www.timeout.com/newyork/food-drink/best-cheap-eats-in-new-york
This one is sortable by area of the city even.
http://realcheapeats.com/nyc
Entertainment
A lot of people when visiting New York will want to take in some kind of broadway show. While most of the theatres have wheelchair access your seating selection is mostly going to be limited. A lot of the time you're forced to sit at the very back , very front or off to a side. If you're able to transfer you might be able to book an isle seat and have your wheelchair moved to the side during the show.
Telecharge is one of the many places online you can book tickets.
https://www.telecharge.com/home.aspx
Other Resources
A Lot of the above information and more can be found in this guide.
http://www.nycgo.com/cms/uploadedFiles/thricenycvisitcom/assets/pdf/access.pdf