Anyone can reccommend a cheap hotel/motel accomodation in NYC/NJ close to NYC

I think Craigslist is your best bet on short term lets. Lots of people in NYC looking to sublet their apartment or room.

I've stayed in Holiday Inn Express in Brooklyn and it was fine and the price was much better since it wasn't in Manhattan, I think they have another one in Queens. In Manhattan I've stayed at On The Ave. To be honest, I don't remember how their rates compare but it was nice and not at all as noisy as staying in Times Square (it's on the Upper West Side, very nice location).

Also Try checking out hotels in NJ near the trains to NYC.

We stayed at the holiday inn express near JFK when we were in NYC for our visa. We took their airport shuttle to the airport every day and then the train into the city from the airport when we needed to. It was cheap but it took about an hour to get to/from the city every time.