We are currently staying in Brunnen on Lake Lucern. We are here for a month and have a car and half off pass. We want to make several day and a few overnight excursions. What would you recommend?
That’s a very open ended question - what do you like to do? What do you want to see?
Switzerland is small, you could literally go anywhere in the country. That is why @wanderweg asks for further information to narrow it down. As you are thinking about that here are some ideas:
Look at myswitzeland.com under 'experiences', ‘events’. Use the filter to see things you are interested in such as ‘customs and traditions’ or ‘wine festivals’. Plan an outing around any that interest you.
With a car and train you have the best of both worlds. You can combine them in one trip, for example to go to the Jungfrau region you might want to drive to the parking lot in Matten by Interlaken and then take the train to explore Wengen, Mürren and Grindelwald.
If you don’t mind driving narrow, curvy alpine roads you can explore areas that are not as easy to access by public transportation and thus have fewer crowds when you arrive there.
One example of a place like this is
https://www.melchsee-frutt.ch/en/
Check out the Swiss national parks for more off the beaten path opportunities:
Schwyz, Altdorf, Stans, Einsiedeln, Arth-Goldau, Rapperswil are some of my lesser-known favorites!