There are no grading services in New York (or at lest none worth taking your coins to. There might be a fourth tier or a fly-by-night in New york but why bother.)
You can't do a walk in grading at the major services home locations for security reasons.
PCGS and NGC do do walk through gradings at some of the large shows. I don't know if there are any in New York next year. They MIGHT do the New York International show in January. You would have to check with the companies. They should be doing walk throughs at Baltimore and Philadelphia. That might be worth a day trip to travel down from New York.
Cost is high. You can find the fee costs for NGC here
http://www.ngccoin.com/services/services.asp (Look at Walkthrough, high value walkthrough and unlimited value walkthrough for US or Walkthrough and high value walkthrough for world coins) and for PCGS here
http://www.pcgs.com/gradinglist.html (Show or Show Express) Looks like a minimum of $100 per coin. For either one you will have to be a paid member which is going to be $50 to $200 depending on which service you choose and what level. If you want to be sure of getting the coins back the same day you should be there when the show opens that day and do not try on the last day of the show. (Note that NGC says same day but also says that current turnaround is 24 hrs so you might not get them back until the next day.
If you are going to be in New York for a month you might want to go to the show for a few days and take advantage of the Express(NGC) or Show economy (PCGS) levels and drop you cost down to $60 to $65 per coin with a 48 - 72 hr turnaround. If you do that you had better be there for the first day of the show.
I don't think anything else would be fast enough to assure you got your coins back before you left for home.