Yangon is the biggest city in Myanmar.
You need to get close to the Aung Mingalar Highway Bus station.
Bus 36 (၃၆) leaves from the north side of the Pagoda and headed directly north up Sule Pagoda Road. It will get you to the Aung Mingalar Highway Bus Station.
Buses 17 (၁၇), 18 (၁၈), 32 (၃၂), 42 (၄၂), 66 (၆၆) all go to the Aung Mingalar Highway Bus Station from parts of the city. Bus 35 (၃၅) goes furthest north of all the buses; it begins right at Strand Rd (riverside) and goes north along the Phone Gyi/Pyay Rd (the next street east of 12th). After the turn left from Khayae Rd onto the Highway (at [16.936N, 96.153E], just north of the Highway Bus Station), there are plenty of places to hitch. The bus takes you another 8.8km north, very near to the toll gate (past the Myanmar Brewery), after which it turns left. Make sure to get off before it turns left there; the turnoff is here [17.0139N, 96.14576E].
You can easily catch a car to Naypyidaw or even straight to Mandalay. If you go to Mae Sot you can take a car only to the beginning of the highway and then turn right. There are also many good hitching spots.