I would agree with helpful person, their suggestion is a good one, the walk from Eigergletcher to Kleine Scheidegg is prob 45min-1hr walk flat/downhill.
An alternative would be Interlaken to Wengen on the train, cable car to mannlichen, walk to Kleine Scheidegg (1.5-2 hours flat walk), then train down to Grindelwald then on to Interlaken.
Another alternative would be train to lauterbrunnen, funicular to murren station then walk along to murren village, flat easy walk less than an hour
Any of these 3 will give you great views of big mountains, the Eiger, the Monch and the Jungfrau.
I'd do one of those options one day.
Explore Interlaken on your arrival and departure days, could probably fit in a lake swim.
Then raft down the Aire from Uttigen to Bern the other day. Go in the morning, picnic lunch on the riverside, then explore Bern, dinner in Bern then train home to Interlaken
However both days with train/cable cars/boats will be reasonably expensive. If you could only do 1 big ticket day I'd do either helpful persons suggestion or my 1st one.
Whatever you do you will see mountains, it just depends how far away they are!