Miles from anywhere, the 10th-century Kızıl Kilise is one of eastern Turkey's most complete Armenian village churches. Now used as a barn, the building uses a beautiful combination of red and black stone and its squat central tower with conical roof and slender windows make it easy to spot if you manage to get yourself all the way to Yağkesen (Kızılvenk) village. As the crow flies that's about 15km north of Ani, but by road it's almost double.
If coming from Kars, take the road turning at the west end of Subatan village. The first 11km from there to Bașgedikler is paved. Just before Bașgedikler take the signposted unpaved road 3km to Oğuzlu, which has a ruinous 10th-century Armenian church. From there to Yağkesen is another 6km on rough tracks. An alternative route allows you to reach Ani without doubling back, using tracks through Ayakgedikler and rejoining the Kars highway at Esenkent.