As far as airports I am partial to JFK. If you do not have the cash to spend on a cab you can take a $5 airtram train to Jamaica where you can catch the Long Island Railroad to Penn Station or take the subways from Jamaica.
I recommend getting an unlimited weekly Metrocard. You will use it quite frequently. Food is Manhattan is expensive in the city but there are deals to be found. For example TGI Fridays will charge you $14 US for a hamburger. That is outrageous. The bars along second avenue are usually crowded. I am partial to the West Village bars around that area. Try the wings at Down the Hatch on West 4th or Off the Wagon. Food can be found for $10 a meal. A pint of beer should cost no more than $6 at ANY bar.
Thrift stores? If looking for clothing bargains, try Filenes Basement in Union Square but you have to go to Macy's on 34th and 7th. There are sale racks all over the place.
Where do I like to eat? Hah - Dinnerwise never the same place twice although there are certain bars I frequent. However I have taken a few dates to a place called Isabella's on the corner of 77th and Columbus. If you are into BBQ try a Brother Jimmys. Places to eat in Times Square Theater District are nice but you are going to pay for it. The one exception is a place called John's Pizzaria which is pizza by the pie only and sit down italian. In my opinion it is better than the food at the overrated Carmines a few buildings away. John's is on 44th between 8th and Broadway. Do NOT fall into the tourist traps, there is no reason to go to ESPN Zone, Hard Rock Cafe, TGI Fridays or anything like that. They are designed to get as much money as possible from you for a hamburger and fries.
If you do not have much money and you want something to tide you over for bigger meal later keep in mind that Subway Sandwiches have a $5 menu for a footlong sandwich. Just buy the drink elsewhere or a bottle of water separately or it will not be counted as a discount. $5 for sandwiches only. If you get the value meal they figure the normal cost of the sandwich in the price.
As far as recreation, bars bars bars, sites - Empire State Building, walk across the Brooklyn Bridge, Statue of Liberty and bring a camera with a lot of memory. In the event you need to get in touch with someone using a computer, there is an apple store on the corner of 14th Street and 10th Avenue, 58th and 5th by FAO Shwartz, and off of Prince Street in SoHo. Oh get a subway map.
LMK if you need anything else.
but i am not a cockney (wanker maybe
