For breakfast, we did best at the cafe on the street a block south of Lucky Dragon and Pyay Strand. It's the first one on the southern side of the road, closest to the river. Their Burmese coffee is good and the puffed buns and fried snacks fill a hole. The staff speak no English, but the owner speaks a little.
A block north, on Kan Street, you'll find May Ywet War Myanmar Restaurant, better known as Auntie Moe's, and this was our favourite place to eat in Kyay thanks to its mouthwatering range of curries. The staff advised us the chilli sauce would "blow our head off" and while that didn't occur, we do advise caution. They are busiest at lunch but a solid option for lunch or dinner. The cafe next door has free WiFi and if you ask nicely they'll give you the password to use while you're in Auntie Moe's.
Along Lanmadaw Street, south of the Aung San statue, are a bunch of beer and food places that are popular both at lunch and dinner. Prices are reasonable and a couple have English menus. Around the corner on Bogyoke Street a night market runs more or less from the railway tracks half the distance to Strand Road and the river front. On the northern side you'll spy Grandma's Restaurant -- we didn't try it but it's a Western-style restaurant offering Western and South Korean food.
If you're looking for a sundowner, Hline Ayar Restaurant, on the riverfront a few steps north of the night market road, is a good option. They also have a comprehensive English menu. We recommend hitting here for sunset, but then moving on as the live entertainment can be, uh, overpowering.
Other riverside options include Southern Star, about a kilometre south along the river road and Romeo Cold Cafe about 500 metres north of the night market, just before the Central Market.
Just off the river, and between Lucky Dragon and Pyay Strand, is San Francisco Restaurant -- it's just about as far as you could possibly imagine from San Francisco.