The down town area is small enough to cover on foot.
Taxi cabs are relatively cheap, starting at around 80NT plus 5NT per .3km.
The city has its own bus system which is decent and covers the major parts of town, but no where near as convenient as Taipei's MRT/bus system.
The train station is in the downtown, and fares are more than affordable.
The new High Speed Railway HSR has a stop near the outskirts of town and can shuttle people from Taoyuan to Taipei in around 12 minutes for around 120 NT. The HSR covers almost the entire length of Taiwan, but a trip spanning the entire length will cost around 2200NT.
Buses run to other cities as well. A bus trip to Taipei will cost 65NT.
