If you decide to buy a round the world ticket rather the cashing in miles (which can be quite a bit of miles for example 200,000 miles for economy on united) you might want to buy a one way ticket and start in Bangkok. I've never done it myself, but apparently you can save quite a bit of money on a round the world ticket by purchasing it in Thailand as compared to the U.S. A travel agent that's been recommended here is
www.chawlatravel.com, but I have no personal experience with them.