I looked at your list and note that you are at the back door to the Rigi when you stay at Vitznau. The cograil up to Rigi Kulm is quite scenic.
The Bernese Oberland destinations, plus Bern, are much better served if you base at Interlaken or possibly Lauterbrunnen, and use the trains. Adelboden is a bit out of the way for the Jungfrau region. There is frequent service, and you would not have to haul luggage.
Have you looked a the timetable?
You will have a 35 minute drive each way as you go from Adelboden just to Spiez. And, then, another 35 minute drive from Spiez to Lauterbrunnen, or 45 minutes to Grindelwald ( which are the two places where you could park your car.
Bern is 35-45 minutes from Spiez. Driving in Bern is an issue if you want to see the old town. And, you'll could still need more time in traffic to get to the old city, because parking in the Altstadt is pretty much non-existent. Your best bet might be the car park by the Casino, on the edge of the old town, although it fills up fast.
Easiest access is by train to the main station, so if you wish to drive you might park at a train station along the route between Spiez and Bern. The train line from Thun to Bern via Belp has a lot of local stops with parking, has two trains per hour, is a short distance to the west of route 6, and that train ride through the Gürbetal to Bern is a pleasant one, through farmlands. It passes Bern-Belp airport on the way. Two trains per hour means that you don't have long waits.
To see that route in the timetable, include "Belp" in the via box, otherwise, the timetable picks the fastest route via Münsingen on a different line with few or no stops.
To see it on a map, use Mapsearch.ch, and zoom in to see the train lines:
Zoom out to see the relationship between Spiez and Bern, (and Adelboden.)
Of course, you could park in Spiez ( we use the underground garage under
the COOP store just across the main street from the station) and take
the fast train to Bern. 3 or 4 fast trains per hour, on the default route through Münsingen offered by the timetable if you do not enter anything in the via box, Takes 29 to 30 minutes.