Provided your expectations are not too high (this is not Bangkok quality) I will recommend Ko's Kitchen for Thai food. Near the the western edge of the Palace grounds. Seems to be popular with the wealthy Sino-Burmese locals. I had a good dinner here last year.
One of the best food memories of my 3-week trip to Burma was the "samosa salad" served by a Mandalay street vendor in front of a stretch of shops selling gold leaf. I'm assuming that you can get this dish in many places; I just happened to try it at that location. BTW: I ate quite a bit of (mostly cooked) street food and in general, I found this to be better than the more formal restaurants. Do not forget to try the fresh sugar cane juice at the stands in Yangon and elsewhere.