A small but genuinely good local museum on Hill Street, repeatedly singled out as one of the best regional museums in Ireland. The standout object is the Cross of Clogher, an 11th-century bronze processional cross with silver and enamel mounts — one of the very few of its kind in Irish hands.
The rest of the permanent collection traces County Monaghan from prehistory through the medieval Gaelic lordships, the Ulster plantation, the linen trade, and the Famine, and ends with a thoughtful section on the recent border experience. Entry is free, the displays are concise rather than overwhelming, and the staff actually know the material. It's about the best 90 minutes you can spend in town.