My husband & I live in Murren for the summer every year and spend most of our time hiking. A few of our favorites...
**Oberberghorn Panorama Trail from Schynigge Platte (red on this map): https://fullsuitcase.com/schynige-platte-hikes/
This ridge hike has epic mountain, water and valley views.
**North Face hike counterclockwise from Allmendhubel (funicular from Murren) - with optional detour to Sprutz waterfall and optional steeper downhill to Gimmelwald or return to Murren for less difficulty -- you can do the North Face hike clockwise RT from Murren but I think the views are better going counterclockwise from Allmendhubel - multiple mountain huts to stop at for a drink or meal along the way
**Birg to Murren via Bryndlii (optional detour to Rotstockhutte): https://www.alltrails.com/trail/switzerland/bern/birg-bryndli-murren?u=i -- This one has epic ridge views and you'll see very few people. Best lighting in afternoon. Ride the Schilthornbahn up to Birg and walk down. The difficulty is based on it being downhill so maybe knees would be a consideration. Have hiking poles.
**Gimmelwald to Tanzbodeli & Obersteinberg - Rated difficult but epic
**If you're up for truly difficult, hiking Murren to Schilthorn is epic, but you need to be prepared for it and leave early enough to catch the last cable down from the Schilthorn. My husband did it in only 3.5 hours but I would say he's a bit of a unicorn and I would plan for 6-7 hours to do it "leisurely".
**Panorama hike from Mannlichen to Kleine Scheidegg with a continuation on to Wegnernalp and optional detour to Falbodensee
This is the easiest hike of them all and will be busier on the section from Mannlichen to KS. Then there will be hardly anyone on it from KS to Wegnernalp. It's more of a walk than a hike and you'll see lots of families on it, but it has lovely mountain views. Optional short detour up to Fallbodensee.
**The ridge hike at Brienzer Rothorn - https://swissfamilyfun.com/brienzer-rothorn-ridge-trail/
From that list, the ones I absolutely wouldn't miss
*Either North Face or Birg to Murren via Bryndlii (they cover a somewhat similar area, both are worth it but if time is limited do at least one of them)
*Oberberghorn Panorama from Schynigge Platte
*Kleine Scheidegg to Wengernalp (the part from Mannlichen to KS is great too, but more crowded)