
to the mountains of Switzerland, Rachel!
One possibility is the
Britannia Hut (elevation 3,030 meters). It is easily reachable in 45 minutes from the Felskinn cableway (a couple of kilometers with almost no elevation gain), or by a 2 hour walk from the Plattjen gondola (4½ kilometers with about 550 meters of elevation gain).
I have read more than once of mountaineers acclimatizing at the
3100 Kulmhotel Gornergrat which (surprise!!) is situated at an elevation of 3,100 meters. It is reachable by train. The views are spectacular (I hiked up for the day in 2008), the prices, alas, are what you might expect in a unique setting.