Try and pick the least popular times to go and times for flying etc... that's often a sacrifice for the cheaper deals as is flying very economy and to airports further out.
Me and my ex got a great deal to New York last year. We end right at the end of August which is the hot season there so not too popular.
We got direct flights from Manchester to NY (Newark) with Continental (probably cheaper from major airports like Heathrow and Gatwick) and stayed in a gorgeous hotel for just under �500.00 each.
Be flexible with dates on sites like Expedia or airline websites and look for hotel deals like extra nights free.
Also booking ahead is a good idea for such destinations as as flights get booked up the prices tend to rise.
I've just had to book for Canada a few weeks ago as the flight I want in September was over two thirds full already and prices rising by the day!!!
Remember to budget for tips as it's a very tipping city, they are not so much gratefully received as standard or even asked for, even for drinks in a bar,