I have only been to Yangon twice, both times for business and both times not long enough to really get a chance to see the city. That said, I found it to be a place that is changing rapidly and plan to return soon for a proper exploration.
In the meantime, I will share my limited number of recommendations:
This hip eatery is located downtown and is popular with foreigners for turning out authentic versions of classic Burmese dishes in a setting that is foreigner-friendly. Interpret this as meaning prices are a bit higher and the flavors possibly a bit muted compared with a local hole-in-the-wall but you are also getting air conditioning, great cocktails and friendly service.
A trio of tasty local salads: pennywort salad in the back left, banana blossom to the right and fermented tea leaf in the front. All three were fantastic and would be good to eat anytime.