Europe in late June?

I have to be in London for work in late June, and am trying to tack a long outdoor weekend on either end of the trip. Haven't ever been to any of the Euro mountain destinations and am unsure of where to start and slightly overwhelmed with options. Any suggestions, hive mind? Some considerations: 1) Best place for quick access from a major airport? Ideally somewhere within a quick train or shuttle? 2) Is it worth bringing skis? I know some resorts stay open, but I'd rather go a bit deeper and get some uphill in...also open to hiring a guide. 3) If no skis, melted out enough in cool places to hike?

Everything looks beautiful, and in a dream world I'd find somewhere relatively close to an airport, hike/ski in, hike/ski a bit, stay at a cool hut for a night or two, then pop back to London after a couple days.

Thanks for any brain power you may have!