Itinerary and base location suggestions for 6 days Swiss trip

I understand the desire to save money, especially in Switzerland, but Bern is about an hour train ride to the BO (Wengen or Murren.) The Jungfraujoch trip is about two hours each way, (at least out of Murren, my reference point.) If at all possible, sleep in the Alps, as your trip has you staying in Swiss cities. You have come all that way, and sleeping IN the Alps is a memorable experience. No one is ever ready to leave the BO. You will never forget the beauty of the sunsets. I love staying in Murren, but there are many advocates for Wengen here.
Not all lifts are open early June, so check out that out in advance. Some of the favorite hiking trails don't open until mid-June.
Enjoy the epic scenery and wising you a trip of a lifetime. Safe travels!

Bern really isn't a good option for your itinerary. I understand wanting to use points, but you're going to be spending 5+ hours on trains every day commuting back and forth from the Jungfrau region to Bern. Depending on what pass you get, you're also going to have extra travel expenses doing this, so if you have it in the budget, I'd strongly recommend staying in Grindelwald or Wengen for your 3 days of activities in the Jungfrau region. Or perhaps you can find somewhere with points in Interlaken?

The most direct route from Bern to Amsterdam is a one stop in Frankfurt. To see times/options, visit SBB.ch/en

It’s not a fun part of travel planning, but the math could help. Add up the transit costs and assign some figure for the time in transit, too.
It may still work out that you would rather stay in Bern but maybe do different things. I’ll put it this way: I’d take a free trip to Bern, but if I were paying, I’d be in a mountain village.

you're going to be spending 5+ hours on trains every day commuting back and forth from the Jungfrau region to Bern.

Check the math by looking at SBB.ch. This is a huge exaggeration, don't let it scare you.

• Bern - Lauterburnnen = 1h 22min
• Bern - Thun = 20 minutes - this is where you can begin your boat journey for Lake Thun
• Bern - Grindelwald = 1 h 36 min

If you were to stay in say Wengen, from there to Grindelwald it is 54 minutes, so actually Bern is only 42 minutes longer.

The only journey that would take a total of five hours is going from Bern up to the Jungfraujoch, which is certainly not something you would do every day. Even from Wengen, it would still take about three hours for a return trip. So it’s not a case of no time versus five hours, but rather just about one extra hour each way.

For anyone who has the money to spend, great, stay in the mountains, but not everyone can and/or wants to do that. Bern is a perfectly good option.