Cardiff grew fast in the coal century and wears that history without costume. The centre is compact, the castle is actually in it, and Cardiff Bay is a modern waterfront at the end of a straight walk or a short train. It is the right first night in Wales, not the whole of Wales.
You can be in the Bannau Brycheiniog in well under an hour, or on a train toward the west. Use the city to land, eat, and hear Welsh in the wild, then go.
See
Cardiff Castle and Bute Park
The grounds are the local park. The house is a Victorian fantasy on a medieval base — enjoyable once you know that.
Cardiff Market
A working market under a glass roof. Lunch here before you look for a view.
The Bay and the Senedd
Walk or ride down. The parliament building is meant to be looked at, and often visited. The barrage path is the local sea wall.
St Fagans
An open-air museum of Welsh buildings, free, a short bus or taxi west. One of the best museums in the UK for understanding a country.