I stayed at the MiCasa Hotel last time. That's near Inle Lake, so it's half-way between the airport and downtown Yangon. A taxi-ride into town still cost only US$ 2.00 and took 15 minutes.

The hotel has internet, which is supplied to the rooms by ethernet cable. In the lobby and the restaurant/bar, they have wifi.

It's a nice apartment-hotel. Have stayed there four times in the last two years. Unfortunately, the prices now have doubled.