Conwy Castle is one of the great medieval fortresses of Europe, and it has the rare quality of being both spectacular from a distance and thoroughly interesting up close. Cadw (the Welsh government's historic environment service) manages the site, and entry gives you access to the full circuit of towers and walls, including the upper chambers of the great hall where the scale of what Edward I built here becomes genuinely impressive.
The castle was constructed between 1283 and 1287 as part of Edward I's chain of fortresses to control north Wales after his conquest. Its design is a masterpiece of military architecture — eight round towers arranged in an inner and outer ward, the whole thing sitting on a rocky outcrop above the Conwy estuary. Along with the town walls, it forms a UNESCO World Heritage Site inscribed in 1986. The views from the top of the towers over the river, the mountains, and the town are worth the climb alone.
Arrive early or late in the day if you can — the castle earns its atmosphere when the tourist coaches have thinned out. Allow at least 90 minutes to do it properly.