Berner Oberland

Bern is a lot further away from the mountains than Interlaken, and most definitely not in the "Berner Oberland". Lauterbrunnen will probably fit your needs. It is in the Berner Oberland.

Have a little look at this map.
The core of the Berner Oberland spans the area between Mürren and Grindelwald. The main villages to stay in are Grindelwald, Wengen, Lauterbrunnen, Mürren. The last three are most people's favorites on this forum, but Grindelwald has the largest selection of accommodation. Wilderswil is a decent backup option, and Interlaken isn't that bad, especially if you are interested in the lakes (Brienz and Thun) and not "just" the mountains.

Bern is a beautiful city, but not at all a good base for the mountains.

I agree with the other suggestions about staying in the Berner Oberland in one of the towns that were mentioned. I usually prefer Lauterbrunnen as a home base, as it's the transportation hub and also central to both sides of the valley. If you'd prefer to be up in the mountains, Mürren is a big favourite with many here.

As you mentioned hiking, you might want to pack along a copy of this book as it provides lots of information on that - https://www.amazon.com/Walking-Switzerlands-Berner-Oberland-Jungfrau/dp/B09SBSFXCW .

Thanks, Ken, for the recommendation. Here is a link to the current edition, 2023.

Walking in Switzerland's Berner Oberland: Easy Walks in the Jungfrau Region https://a.co/d/fPthm6l

There are more than 4 days of activities in the area. It makes most sense to stay in one of the towns in the 2 valleys. Interlaken is a better week home base if you expand your activities to the two big lakes and the other valleys of Kandersteg and Meiringen. Price and availability may affect your choice.

I would stay in Lauterbrunnen…..right in the middle of the valley and easy access to the train station for excursions….and plan a day trip to Hotel Geissbach on a boat from Interlaken and eat at their delightful restaurant!