Do you climb / scramble – I hear Wales is pretty good for that sort of thing….. 😉
+1 for Cae Du, though you might need to use the car to get to places you want to ride. We stayed at Dolgellau recently, grim town, but you can ride to CyB from there and Dyfi stuff is nearby too.
Cadair Idris if you want a big mountain without a voluntary bike ban.
Off the bike and not climbing; Lots of twee steam railways, good walking obviously, Port Meirion (Prisoner town), castles at Beaumaris and Conway, etc. Sorry, struggling a bit as I only really go there to ride and climb.
You could take a look at the Plas Y Brenin website and get some ideas of other things to do or book on one of their courses (do your SMBLA training!)
Take a brolly.