GPX files can be downloaded at the bottom of this post (you'll need to register for this). No guarantees of accuracy given or implied. your mileage, quite literally, may vary
Snowdonia 212 miles
Elan Valley 102 miles
Brecons 183 miles
Or adapt the above, Elan Valley route probably the most suitable, to include a stop at the seaside for ice cream. Aberystwyth seafront, Aberaeron or New Quay are possibilities.
Weather in Rhayader for the next 5 days