I read it as Llanynys, Breconshire? It's a small village on the Afon Irfon, close to Builth. It's sometime seen as Llanynis.
"LLANYNYS, a parish in the hundred of Builth, county Brecon, 3 miles W. of Builth, its post town, and 4 N.E. of Llangammarch. It is situated on the river Irvon or Irion. There is no village, only a few farmhouses. A great part of the surface is mountainous and comparatively barren." (National Gazetteer, 1868)