the first 2-3 weeks in May.
Just to clarify, do you mean you will have a shorter holiday sometime during the first two to three weeks, or that your trip will last for that duration?
If it's the latter, that's great because you will likely face a variety of weather and a longer trip gives the possibility of more spectacular days mixed in with rainy/cloudy ones. This past spring was not the greatest in that regard, but spring in the Alps can often be stunningly beautiful!
You'll certainly have plenty of hiking options to choose from. For fun and inspiration, you can check out Switzerland Tourism’s 10 Hiking Facts That Will Amaze You to get an idea of how vast and varied the hiking trails are in Switzerland. You’re by no means limited to the few favorites in the Jungfrau Region - but even with those, some are open all year round, such as the walk from Grütschalp to Mürren, on from there down to Gimmelwald, plus all of the walks in the village of Wengen.
https://www.myswitzerland.com/en-ch/experiences/summer-autumn/listicles/hiking-facts-that-will-amaze-you/
I took a look at the feedback you received on TA, and I think staying near Lake Thun is a fantastic idea at this time of year. Someone suggested Spiez, which is great in terms of access to transportation to various other locations, but your own choice of the Beatus Wellness Center will give you a much more spectacular view. While you'll need to take the bus to Interlaken or Thun to explore other areas, it’s a beautiful location to enjoy local hikes, take a boat ride on the lake, or simply relax and admire the scenery.
During your stay you can expect:
- Green fields
- Snow-capped mountains
- Wildflowers in bloom, including dense fields of daisies or poppies
- Spring blossoms on trees
- Canola fields in bloom
- Cows out grazing
- Waterfalls at their peak
I would check the tourist websites for each location that you are thinking of. Most of them will list local hikes and also the times of year that are best for those hikes. Cycling is also a really great option at this time of year.
As I mentioned already, you can of course, encounter rain, cloudy days and fog. If you’re hoping for a mix of outdoor activities like hiking or cycling and indoor pursuits like visiting museums, this could offer a good balance.