One of the nicest and affordable hotels in Yangon is the Kandawgyi Palace situated on the Kandawgyi Lake. Shop around on the internet for the best rates. I normally pay around Euro 55 - 65 per night for 2 persons including breakfast. Of course, there are many cheaper hotels in Yangon, but the KPH, especially on arrival, is clean, quiet, has a swimming pool, free internet for guests, and the most magnificent garden. It was at one time during the time of the British the home for the botancial and natural history museum. A great place to overcome jet-lag and if you are awake early, the lake and its long wooden bridge comes to life way before dawn. With the rising sun and the mist floating over the lake its a perfect photo opportunity and you dont even have to move from your room.
I may add that the Shwedagon Pagoda is 15 mins walking distance from the hotel.