You could fly from Great Falls, Montana to Macon, Georgia for $994 US Oct 1 to Oct 8. The best thing to do is go through United's timetable and look for the smallest out of the way places with the lowest frequency and try to connect to another airline with a similarly low frequency to another out of the way place. Use Travelocity or EasySabre to do a fare search -- it will show you all of them for each city pair on any given set of dates.

Before putting too much work into it, check that the free ticket is redeemable for something--a lot of prizes are non-refundable non-exchangeable etc. etc.