Alongside magnificently dilapidated earthen sections of the Great Wall that disappear over the top of Horsehead Hill (马头山, Mǎtóu Shān), a fabulous Gothic church ruin is quite a sight. All that remains of the Holy Mother Church (圣母堂, Shèngmǔ Táng), built in 1876, is its front gate and bell tower and lopped-off spire above it. No explanation for the church's demise is given in the blurb on the board alongside, nor how the church arrived in such a remote spot.
Fourteen recently built stations of the cross lead the way to the church ruin. You can hike along the wall for some thrilling views, but pack water.
This entire area is very near the border with Inner Mongolia. To reach Bā Táizi, hop on a bus (¥18, 80 minutes, regularly 6.15am to 6.20pm) from Datong's main bus station to Zuoyun (左云), then negotiate with a taxi driver to take you to Ba Taizicun (八台子村), around 20km away. Expect to pay between ¥80 and ¥120 return; the driver will wait for you for around 30 minutes. If you want to spend longer hiking along the wall, you will need to pay the driver more to wait for you.
If you ask nicely (or cross the driver's palm with a bit more silver), the driver may take you up winding mountain roads to a scenic lookout on top of Motian Ling (摩天岭), on the road to Liangcheng (凉城), where you can get an elevated perspective down onto the earthen Great Wall trailing off into the distance.
The last bus to Datong leaves Zuoyun at 6.30pm. You can also get here by taxi from Datong via the Great Wall Scenic Road.