Getting there probably means flying in to BKK then getting a regional flight to Phuket. You can go through Japan, Taiwan, Hong Kong or Singapore or KL even, if you're of such a mind. What is closer to you, Los Angeles/San Francisco or New York? You can get one-stop flights from LA/SF, passing through a range of cities like Seoul, Beijing, Taipei, or Hong Kong. There are also flights going east through Europe that will pass you through Frankfurt, London, Amsterdam or Dubai. These are more likely flying from New York/Newark. When I went to BKK, I flew from Newark to Seattle, Seattle to Taipei, then Taipei to BKK. It was the same plane from New York to Taipei, with just a short layover in Seattle to change crews and clean the cabin. There was about 20 minutes on the ground in Taipei, enough to get from the one gate to the next, then we were up in the air again. Landing in Taipei is a little hairy, as the plane has to come in fast and hard, and when you're taxiing to the terminal you can see the anti-aircraft missile emplacements. A few years later I went to Singapore and Cambodia, and that flight was DC-New York-Amsterdam-Singapore. That's a LONG flight, but logistically easy once you're out of the US. The pain in the ass is getting from DC to Newark - you have to change terminals at Newark (and at JFK) and go outside to get from your domestic flight to the international flight. And they no longer check your luggage through, so you have to retrieve it and haul it yourself from terminal to terminal.
No matter how you cut it, it's going to be a LONG trip (about 18-24 hours each way). I don't know that flying through Beijing, Shanghai, or Guangzhou vs. Tokyo will really make a difference in the experience.