In reply to MuckyMorris:
I would recommend the Wengen, Mannlichen, Kleine Scheidegg tryptich-accommodation available in Summer at all 3 points. Perhaps not as majestic as the more glamorous, & more famous, Eiger, Monch, Jungfrau tryptich but they still offer a spectacular view.
The walk from Mannlichen to Kleine Scheidegg under the Eiger is very well engineered & contours the mountainside so no big ups or downs, overall it is downhill. See here:-
https://map.wanderland.ch/?lang=en&bgLayer=pk&logo=yes&season=s...
Transport easy (though I believe engineering work is going on Summer 2019 on the Grindelwald side for the new gondola). A stay at Mannlichen or Kleine Scheidegg would certainly fit the 'hut' bill in terms of location & scenery.. ..but far more civilised than a hut. My choices would be here:-
https://www.berghaus-maennlichen.ch/de/Sommer
or here:-
https://www.scheidegg-hotels.ch/index_e.php
the latter hotel is better if you like watching trains.. ..and being at the foot of the Eiger Nordwand. At least an order of magnitude more spectacular & atmospheric than the Gemmipass from the Kandersteg side. The maennlinchen is far more hut like in terms of isolated situation but nothing like a hut in terms of creature comforts.
Wengen is very close to Interlaken & easily accessible from either Zurich or Geneva-I far prefer the Zurich route. Select to travel to Interlaken via Luzern & Meiringen over Brunigpass rather than round the houses (flattish ground) via Bern. Stunning scenery & an adventure in itself.
I wish you & your wife well
Mike