Britain's two best mountain playgrounds sit only a few hours apart, and you can link them without a car: the Lake District's fells and lakes, then across to Eryri — Snowdonia — for Wales's biggest ridges and slate-village culture. A week does it well. Costs are the usual UK story: transport and beds sting (hostel dorms 22-35 GBP, YHA and independents), but the hills themselves are free and there is no entry fee to any of it.
In through Manchester
Fly or train into Manchester, which is a better city break than it gets credit for — Northern Quarter record shops, the Science and Industry Museum, and some of England's best cheap food in Rusholme's curry mile. But the hills are calling: direct trains run to Windermere in under two hours (from about 15 GBP booked ahead).
Windermere and Ambleside
Windermere town is the railhead; the lake and the walking start immediately. Warm up on Orrest Head, the 20-minute viewpoint climb that made a young Alfred Wainwright decide to spend his life cataloguing these fells. Take the boat down England's longest lake or the open-top 599 bus to Ambleside, a solid hostel base. From there, the Fairfield Horseshoe is the classic full day — ten miles of ridgeline — while Loughrigg Fell gives you the postcard panorama for a fraction of the effort. Refuel on Grasmere gingerbread from the tiny shop by St Oswald's churchyard, where Wordsworth is buried; the recipe has not changed since 1854 and the smell reaches the street.
Keswick and the northern fells
The 555 bus to Keswick is 40 minutes of the best scenery any local bus in England covers, over Dunmail Raise past Thirlmere. Keswick sits between Derwentwater and the big northern fells. Catbells, straight across the lake by launch, is the perfect two-hour ridge for a lazy day; Blencathra via Sharp Edge or Skiddaw for a proper one. Evening moves: a swim from the Derwentwater shore if you are brave, then the Dog and Gun's goulash and a pint of Loweswater Gold. If it rains — it will rain — the Theatre by the Lake and the Puzzling Place will absorb an afternoon.
Across to Wales
This is the one fiddly leg: bus or train back via Penrith and change at Chester and Bangor for Llanberis, about five to six hours all told (25-35 GBP). Watch the transition — drystone Lakeland gives way to the North Wales coast castles, then the mountains shoulder in and the chapels and slate tips announce you are somewhere culturally distinct. You will hear Welsh spoken as the default in shops around here; a diolch (thanks) goes a long way.
Llanberis and Yr Wyddfa
Llanberis crouches under vast slate quarries at the foot of Yr Wyddfa (Snowdon), 1,085 metres, the highest peak in Wales. The Llanberis Path is the long gentle way up; the Pyg and Miners' tracks from Pen-y-Pass are better walks (get the early Sherpa'r Wyddfa shuttle bus — parking chaos is real, and the shuttle solves it for a couple of pounds). Miners' up, Pyg down, with the glacial lakes of Llyn Llydaw and Glaslyn below you, is the ideal circuit; confident scramblers take Crib Goch's knife-edge instead, and should only in dry, calm weather. The summit cafe means you may share the top with train passengers — start at dawn and you will have the ridge to yourself and a cloud sea below.
Spend your spare day on the National Slate Museum (free, and genuinely moving on quarry life), a dip at the blue lagoons, or the Ogwen Valley's Tryfan, the most fun 918 metres in Britain — hands-on rock the entire way.
When and how
May, June and September are prime: long days, midge-light, school-holiday crowds absent. Book YHA beds ahead for weekends. Carry waterproofs always, cash never — even the summit cafe takes cards. Finish by train from Bangor: London is three and a half hours, Manchester two.