Dear Hivemind, I'm planning an epic trip of rambling across the UK countryside with my mother this May and June. We have two weeks, and here's the itinerary I had planned:

London - Bath - Cardiff - northern Wales (hiking) - Lake District (more hiking) - a bit of Scotland (Glen Coe and Isle of Skye) if we have time.

We're all set for plans and accommodation in London and Bath. Alas, turns out there's a beer-company-sponsored football thingy happening in Cardiff, and not only is everything in Cardiff booked, but I've also had miserable luck finding places to stay in northern Wales around Brecon Beacons. I've scoured fifty million websites, but they all say everything is booked - although some of them are suspicious enough that I'm not sure if the places are actually booked or if the system is just broken.

Anyways, any recommendations on places to visit and, even more importantly, to stay in Wales or the Lake Disctrict? One big limitation is that we don't drive, so we need to be able to get relatively close using public transportation and take a taxi the rest of the way. I do love castles and Georgian manors, but what we're most interested in is lovely areas to hike around in. I've visited a bunch of cities across the UK, so I'd love to discover smaller "gems".

As always, any and all tips will be received with excuberant gratitude.