St Cyngar's Church stands on a low rise above the town centre, on a site that has been a place of worship since early medieval times. The town's name — Llangefni — means "church on the river Cefni" in Welsh, and this is the church in question, named for a 6th-century Celtic saint. The present building is largely Victorian restoration, though the site's history stretches back over a thousand years.
The churchyard is worth a quiet wander for its old Welsh-language slate gravestones. The church is usually open during the day, and the view from the churchyard back over the town gives a sense of the low, central Anglesey landscape. It's not a grand building, but its position gives it a quiet presence at the heart of the town.