Wengen and Murren

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There is no bad choice here, but stay all nights in one location. A recent poster reported that the construction hasn't been much of an issue lately.

Use booking.com to research available lodging within your budget. That may help you make a decision.
Oh, after your research, and you've made a choice, book directly with the hotel. I have found better prices when staying 4-5 nights in one establishment, vs two nights. ( No guarantees.)

Enjoy this beautiful country!

It only takes 45 minutes to get between the 2. Pulling up stakes and repacking is a chore, Plus you might get a better deal on lodging with a 4-night stay than two 2-night stays. Anyway, the journey is half the fun, You could take the train down to Lauterbrunnen, then the detachable gondola to Gruetschalp, then another short train ride to Muerren. Or, from Lauterbrunnen, take the bus to Steckelberg and ride up in the 2-stage cable car. Go one way one day and the other the next, or return different ways.

https://www.jungfrau.ch/en-gb/corporate/jungfrau-railways/jungfraubahn-holding-ag/bergbahn-lauterbrunnen-muerren-ag/

Looks like it!

With only 4 days it does not make any sense to move. Just choose one—-both are good options.

You can get lots of opinions, and reasons for those opinions, from this thread:

https://community.ricksteves.com/travel-forum/switzerland/wengen-vs-murren#bottom

I will just add, if I didn’t say; in that thread, that we spent 5 nights in Mürren last September, and the only effects of the construction we experienced were (a) walking down to Gimmelwald on the road, there were more trucks and tractors than usual, (b) when we hiked the North Face Trail, we had a bit of trouble finding the actual trail where it pass through the construction site, and (c) the main entrance into the building where our apartment was situated was closed, so we had to use an alternate route.

But otherwise, no noise, dust, or other effects.

Construction in Murren is going to be going on for another couple years. They are finishing the train construction, but the Schilthorn construction won’t be complete until 2025 and they started work on the new Alpin Palace Hotel/Condos, which is going to take probably through 2025.

The works on the railway are pretty much finished. New trains will be delivered this spring (one has already been delivered in Fall) and we should get a faster schedule next year, once they have retired the old trains.

The Schilthorn construction will continue in to 2025. The new cable car from Stechelberg to Murren should start operating in Fall. The noisiest part of that was at the start, as they were demolishing stuff, and having to drill through rock etc...

The Palace building site should not be that noisy. And it is good that they are finally doing something with that building.

There is also someone trying to get a project in the village, where the old Kurhaus used to be, but that is something that has been dragging along for ages... You will notice the profiles however when you walk through the village.

I would pick Wengen and visit Murren for a day. Just a preference because I like the way Wengen is laid out as it is more compact. Murren seems very stretched out to me to visit restaurants, etc. Keep in mind during the day you will be out and about, so where you stay only affects your evening hours. Even the construction shouldn't be an issue unless you plan on spending your entire 4 days within Murren. I assume there is no construction happening at night and in the evening.

I would not split up four nights. Stay in one place and just visit the other for the day. Both have great views, access to hiking, etc.