Best of the best around Murren

Since you're there a short amount of time, skip Trummelbach Falls (in the valley) unless you wake up to complete cloud cover or rain. Definitely take the gondola up to the Schilthorn for the views if the weather is clear.

Mannlichen to Kleine Scheidegg hike.

With such a short time there, you will have to choose from many choices.

Are you interested in the adventure events, like bungee jumping, the via ferrata, hang gliding, etc.?

Or are more boots firmly in contact with earth? I get that you want to do plenty of hiking. High or low?

Or trains?

Not really into adventure events. I'm ok with either high or low hikes. I'd just like to see as much as possible on them. I am thinking we'll have time for two 4-5 hours hikes, as well as one excursion (Schilthorn if sunny, Trummelbach if raining). Does that sound reasonable?

When you get to Mürren, look around for the trail maps that are all over the place (ask hotel if you don't see them). It will give you enough info on trails, their degree of difficulty, and length of time, to help you decide. It will be much clearer once you are on the ground and oriented, and also see the weather. We took the gondola up the Schilthorn. The hike looks strenuous and time consuming, but also very dependent on the weather for safety.

I did not think the Trummelbach Falls were worth it BTW.

Trummelbach Falls *is beautiful! Did a easy hiking out of Murren but I can't tell you which trail.

One nice "hike" that you could do is take the Allmend-Hubel Funicular up the hill, and then walk back down through the tranquil alpine meadows. There are a couple of bars / hotels along the way where you can stop for a cool one (assuming they're still open - it's been a few years since I was last up there). It's an easy stroll, and all downhill and should take a couple of hours.

Two hikes and an expedition to the Schilthorn is doable, weather permitting.

Day of arrival, once you drop your stuff at the hotel, assuming great weather, head down to Lauterbrunnen then up to Wengen on the little train. From Wengen take the lift to Mannlichen, hike to Kleine Scheidigg and if desired back down to Wengen. Otherwise take the train at KS and backtrack to Muerren. Check the last lift time at Grutschalp. I think it is after 18:00 this time of year, but best to be certain.

Thursday, if it dawns clear, head to the Schilthorn. When you come down, hike back toward Grutschalp along the rail line, take the cableway down to Lauterbrunnen and walk back through the valley, stopping at Staubbach Falls. Cableway back up at Gimmelwald and then to Muerren, although you can also walk up to Muerren from Gimmelwald.

This plan gives you hikes on both sides of the valley, although each hike is far less than 4 hours.

With your limited time I would suggest just staying in Murren and doing one of the many wonderful hikes that leave directly from the village. The TI office in the Murren sports center can provide you with local trail maps and help with trail conditions.
One of our favorite day hikes is from Murren to the Rotstock mountain hut. This hike is about 12 kilometers, round-trip, with wonderful views all the way. It has one steep climb and a few rocky descents, but nothing technical or too strenuous, and the views looking out from the Wasenegg ridge across the beautifully desolate valley toward the Schilthorn are worth it. On the trial out, stop at the cheesemakers hut at Schiltap. Then have a leisurely lunch at Rotstock hut before you head back to Murren via the ridge trail that descends to Spielbodenalp and Gimmeln, where you can have an afternoon coffee and kuchen. Once back in Murren stop at the Staeger Stuebli in the center of town for a spritz before dinner on the terrace at Hotel Eiger.
A perfect day!

"It will be much clearer once you are on the ground and oriented"

I just want to emphasize this point. Before I went, I found it very hard to understand the options from the RS book, the maps, etc. Once you're actually there and seeing it in 3-D, it's ten times easier to understand.

I second the recommendation of the Allmendhubel.

We loved the North Face Trail from Allmendhubel with the additional hike through a forest to the Sprutz Waterfall. Be sure to stop for lunch at one of the farms.

Thank you all for your replies. We just arrived back and had a lovely time. Day 1 we did the Northface Trail but took the detour to the Sprutz waterfall. Day 2 we hiked to the rotstockhut and then continued up to the top of the Schilthorn. Took the cable car down and had some time to wander around the shops in the village. I really appreciate all the help I received from this board!

May I ask where (which hotel) you overnighted? Also what you liked (or didn't like) about it. Any advice to others going?

We stayed at the Hotel Alpenruh. I loved it - we had a lovely terrace overlooking the mountains, and the staff was very helpful and accommodating. We didn't eat at the restaurant there (except breakfast), but I would like to try it if we return. In terms of advice to future travelers:
- The hike from Murren to the Schilthorn via Rotstockhutte was doable and provided amazing views. It took us 5 hours with a half hour break. However, the last hour was a bit scary for me. As I have read in other posts, the trail is wide enough, but if you are funny about heights there are a lot of places with steep drop offs on both sides. I probably would have been more comfortable if the trail hadn't been so muddy and if there had been a few more people on it (it was a Thursday morning, so not crowded). But I am glad we did it!
- The Sprutz waterfall was great. It was a steep, muddy trail, but I really enjoyed it. We didn't go to Trummelbach or Staubbach but there are plenty of waterfalls you see just hiking.
- If you are traveling with kids (ours stayed home) the playground at Allmendhubel would definitely be worth it!

Thank you very much for sharing your experiences!