Taxis are very cheap and plenty in rangoon, quite scary at night since somehow the turn off the front lights god knows why. However it beats any alternative since renting a car is not possible (there is not rent a car agencies) the Bus are overcrowed and dangerous. The best bet is to find a taxi man that can provide limousine services, There are plenty of those too, for a daily price they will take you anywhere in rangoon and wait for you if necessary ( something around 50 US dollars wil make it).
The taxi fares in Yangon are relatively fixed - and there is little room or need for negotiating fares.
They are, one and all, relics of at least 30 years of age, but we found this mode of transport very easy to get around with. The drivers were generally courteous, and had enough English for directions and even small talk. Never mind that the windows often don't work - and airconditioning is a rarity.
Taxis seem to be the best way to get around. A taxi fare inside the city costs between 700 and 1000 kyat (USD 0.80 - 1.10). Remember to agree on the fare before you get in as there are no meters.
The taxi drivers will quote a higher price when you first ask about your destination, so some bargaining may be necessary. I had one taxi break down and one taxi driver get lost, so I guess it's pot luck. All part of the fun!
Busses ferry ppl around but are always crowdy and one shd try the cabs which one can easily find and most of the places can be reached at $1 or less- unbelievable but true.
There are the rickshaws in some places to et around the city.