(2-part post):
Jno mentions that the US authorities might require a return ticket. They may do, depending upon whether you've got a visa or not.
If you'll be travelling under the Visa Waiver Program (by applying for an ESTA, online, at least 72 hours prior to travel) you
must have a return ticket. Otherwise you'll be refused entry (or, more likely, the airline won't permit you to fly):
http://www.usembassy.org.uk/cons_new/visa/niv/ vwp3.html
If you've got a visa, you do
not require a return ticket:
http://www.usembassy.org.uk/cons_new/faqs/faq_ visa_niv.html#niv070
Open-dated return tickets usually cost far more than the cheapest fixed-date tickets. It might be better to buy two single tickets. However, some airlines charge more for a single ticket than for a 'fixed date' return ticket.
Most airline websites don't allow to buy open-ended tickets online. So it's probably time to pick up the phone. Try these numbers:
0800 414 767 (Delta Airlines, Edinburgh to JFK, New York)
0845 607 6760 (Continental Airlines, Glasgow & Edinburgh to Newark, New York)