Buses are cheap: Y1 - Y1.5 for most journeys. For bus routes, the best thing is to try to buy a city map (Y3.5) from a newsstand. If you are comfortable navigating a Chinese website, then the routes are available at the Mapabc site. Here is an example, showing the route for bus #1. Try cutting and pasting two place names from this site into the from-to search boxes (xxx 倒 xxx), and you'll get some suggested bus routes, as well as tips on how to complete your journey on foot at either end.
Taxis aren't too expensive either. The meter starts at Y7 for the first 3 km, and then it's Y1 per km after that. Y10 - Y15 can get you quite far in the city.