The only direct flights to the USA from Newcastle (according to the Newcastle Airport website) are with ThomsonFly. This is a weekly service to Sanford and therefore not of much use to you.
So you're forced to fly via a European hub airport, such as Heathrow, Dublin or Amsterdam. The best choice might be Dublin. You can get there really cheaply with both Ryanair and Aer Lingus. (However, Aer Lingus doesn't show the route in their schedules after this summer and Ryanair haven't yet published their summer 2008 schedule. Remember, also, that if you use a 'point to point' budget airline to connect with another flight, you need to build plenty of connection time into your schedule because the 'point to point' operator won't help if you miss your connection).
Assuming you can get to Dublin cheaply, Aer Lingus offer an inclusive return fare to JFK, on most dates during the period you specify, for �624 (about �430). There are cheaper fares on a few dates. Alternatively Continental will fly you to Newark, on most of your required dates, for an inclusive return fare of $776 (about �390).
Chris