if you want to do it with one mileage run trip, you'll probably have to go to Asia. That may be tough for under $1000. With creative routing, you might be able to do it with one trip to central/eastern Europe or two transcon trips.

I recently did CLD-LAX-EWR-SJU(San Juan) then back via IAD and LAX on a Y fare for about $400, earning 9000 PQMs. I don't know if anything like that is still available now though. If you are already elite, flying out of CLD is often great for mileage runs because you earn 500 PQMs for that short flight to LAX (all UA flights out of CLD go to LAX).