U.S. Air Force definitely maintained air bases in Thailand during the 60's and 70's. Have several friends who flew out of there. Don't remember when the last base we had in Thailand closed, but it should be easy enough to look up.
I don't think we had air bases in Burma, at least not since the end of WWII, but it would not have been surprising for there to have been flights into Burma during the 50s and 60s for training exercises with the Burmese military. Probably not a regular stop for the USAF though.
Re: Singapore - Obviously no bases there, but I'm sure it could have been a refuling stop between SE Asia and Australia during that time period. C-47s and C130s had decent range with fuel, but probably not that good. We had good relations with Singapore during the time period you're referencing, so I can't imagine why we couldn't have landed there.
