My surname is Welsh and in 2017 we visited South Wales and the village in Cardiganshire north of St. David that my ancestor left in 1716 with his two brothers to come to America.
South and North Wales are both amazing. For South Wales, I recommend a couple of days in Cardiff. Cardiff Castle, the Museum of Welsh Life and Caerfully Castle (a short train ride from Cardiff) are great. There are several castles near Cardiff as well as Tintern Abbey close to the English border.
Tenby, Wales is wonderful. We stayed there and on our way to St. Davids, we visited Pembroke Castle. There are some very scenic places in S. Wales.
In North Wales, Conwy and its castle are a must see. Snowdonia National Park is great. Caernarfon Castle is another you would likely want to see.