As the other posters have said, I would avoid booking through a travel agent, you are paying a premium for having someone do for you what you can very easily do yourself. €500-700 each would be doable for four nights, January-March is the cheapest time to go to New York because it is normally very cold, so you should get flights for less than €500 each and a hotel for €100 per night (presuming you are sharing a room here).
For flights, check out prices on www.skyscanner.com
both these sites will check all the airlines for the best price. Don’t feel you have to stick with Aer Lingus, Continental, Delta and US Air can sometimes have really good prices. It’s probably a little early to get the best flight prices, I find 6 months out is the best time to book, but keep checking, you may hit on a bargain.
It is definitely a little early to book a hotel, the best deals aren’t announced until a couple of months in advance. Trip Advisor is your friend here, there are some awful sh*t hole hotels in New York, so check out hotels here before you book:
Travelzoo is good for off peak season bargains, but it is too soon for those, you can sign up for their news letter and weekly deals sent to your inbox.
If you are nervous about leaving your hotel booking til the last minute, you could book something that can be cancelled now and then cancel if something cheaper comes up.
is a great site – most of their hotels require no deposit and can be cancelled, but just check the terms of booking before you book.
If you could stretch the budget a bit, I’d be inclined to maybe spend an extra night or two, four days is a bit short for a first time in NYC, it’s a huge city with loads to see and by the time you lose the first day travelling, 4 nights would only leave you with 3 days. For the sake of paying an extra bit on hotels, I’d be tempted to stay at least 5/6 nights.