Hang Chat is a town in Lampang.
Hang Chat is the center of a district 20 minutes outside Lampang. It is worth a look if you have your own wheels. There's not much to see, but a lot of tasty things to eat and some Lampang-themed stuff to buy.
The best way to get into Hang Chat is by having your own transportation. By car or by motorbike, take Highway 11 (the superhighway) towards Chiang Mai. If you are having trouble finding your way to the highway, pull over and ask "Chiang Mai, yu tee nai khrap/kha?" (i.e., Where is Chiang Mai?), and a local should set you on the proper path. Once you're headed the right way, be on the lookout for the sign indicating where you need to u-turn into the town. The turn is well-marked. Once you make the u-turn, follow the sign to turn off the highway to the left. Congratulations! You've made it!
Alternately, if you are staying to the north of the river in Lampang, you can take 1039 straight into the heart of town.
You can also take a green (regional) bus headed towards Chiang Mai from the bus station in Lampang. Buses are un-air conditioned with hard seats, but you won't be on it for very long! Ask to get off at Hang Chat and they'll drop you by the side of the highway at the bus stop near the Shell gas station. You can then explore the town on foot. This may be more trouble than it's worth, however.
You can walk around on foot or use your own wheels to get around. The center of town is not very big, taking maybe 15 or 20 minutes to walk end-to-end.