Llangefni is the county town of Anglesey, sitting quietly at the island's centre away from the coastal tourism that draws most visitors. It's a Welsh-speaking market town without much to detain you, but it has one genuinely good reason to stop: Oriel Ynys Môn, a museum and gallery that covers the history and art of the island from prehistoric times to the present. The permanent collection includes work by Charles Tunnicliffe, the wildlife artist who lived on Anglesey for decades, and there are good temporary exhibitions throughout the year.
The town is also the administrative hub for exploring the rest of the island — a short drive in any direction brings you to Iron Age hillforts, Bronze Age burial chambers, and the coastal scenery that makes Anglesey worth visiting in the first place. Just north of the centre, The Dingle is a sheltered wooded valley good for a short walk, and Llyn Cefni reservoir is a calm birdwatching spot a couple of kilometres further on.