The Panoramaweg hike is well-described on the hikingwalking.com website, but in the opposite direction, from First to Schynige Platte:
Maybe they go that way because it is slightly more downhill. But the trail has little ups and downs the whole way, without a lot of elevation gain or loss in total. I like the way we did it, from Schynige Platte to First, because the views were wonderful, and by ending at the First gondola and riding down at the end,we had the opportunity to stop for dinner in Grindelwald before returning to Mürren. There are a number of good restaurants in Grindelwald, including the oddly-named but very good Onkle Tom's Hütte, which (if it still exists) is a nice casual place with outdoor seating and excellent pizza and salads.
I have particularly fond memories of that hike because while walking through Grindelwald after dinner we heard the beautifully haunting sound of yodeling (which is not at all the jokey-sounding "yodel" you may have heard, but rather lovely a cappela harmonized singing, without words.). This is a popular social activity in .switzerland; even competitive. This was a group practicing, and they were seated at an outdoor table in from of a hotel, yodeling while the hotel supplied them with glasses of beer. We found 2 seats at a shared table and sipped a glass of wine while enjoying the impromptu "show".
Back to hiking. One of my favorite hikes directly from Mürren is the North Face Trail, not to be confused with the Eiger Northface Trail near Grindelwald ( that one goes from Eigergletscher stationnon the Jungfrau Railway down to Alpiglen passing below the infamous North Face of the .Eiger).
The Mürren North Face Trail connects the top of the Almendhübel funicular with Mürren in a long sweep outward and back, above Gimmelwald. It is dotted with signs discussing the history of mountaineering in the area, with first ascents of the various peaks you see across the Valley. I think it is the same as the M2 hike described on the Lauterbrunnen website linked above, although they don't call it the North Face Trail.
If you Google the name of the trail you will find many descriptions, starting and ending different places, and covering both directions. We did it anti-clockwise, from Allmendhübel back down to Mürren, although we hiked up to Allmendhübel rather than riding the funicular. You could make it a half-day hike by taking the funicular.
This blog took the same route ( starting at the top of the funicular) has photos, including photos of the signage for the trail:
Just to give you more options, here is a website with more hike suggestions (and photos), starting from Gimmelwald just a short walk down the hill from Mürren:
We like the circular hike to Rotstockhütte and the Sefeinental (7th hike in the list), although it was a bit muddy in parts due to cow activity ( our hostess at Chalet Fontana warned us of that).
The Gimmelwald down to Kilchbalm (or Chilchbalm) hike (4th hike on the list) is another good short hike, especially if you are looking for a rainy-day activity.
I have always wanted to do the hike to Oberhornsee (3rd on the list) but haven't been able to make time for it yet. Need to go back . . . .