Actually this sounds more like a vacation than a mileage run. If you're looking to fly somewhere and see the place and you're budget is $1000, I tihnk you're best bet is Bangkok and then travel around Thailand.

Once there you can live rather inexpensively, so your money will be able to last. Frankly, I think you could do a month in Thailand for a little bit more than that.

Of course, the main topic here is flying in order to rack up miles aka MR. That being said, BKK is certainly one of your furthest destination options that is doable for under $1000.

Come poke around in the ASIA forum if this interests you. Thre are lots of people that can give you ideas.

Cheers, Scho