I opened the map for the Tell-Pass, and found that it covers a lot larger region than I expected:
I can see why you would like to use it as a way to define an exploration area.
I also did a very skimpy quick search for lodgings in Brunnen and found very few.
Your logic for picking Brunnen is probably the combination of a really beautiful location on the lake, plus good train service on the 600 line. Frankly, I am surprised that there are not more offerings.
Once with family, we used the Swiss Holiday Park in Morschach. You do pay for the facilities and convenience, and we used a car to get to Brunnen station, as well as some other trips,even though there is good bus service once per hour. So, I don't think it meets your needs.
I looked over the map of coverage, and find very few places with train service more frequent than once per hour that are on the lake. Flüelen might work. Also, there is a local now that runs from Erstfeld north, and the pass coverage goes that far south. But, it is not on the lake.
Another thought is the coast near Merlischchachen, but the train service is is only hourly, but twice that if you count both directions. And, it is likely higher priced, due to proximity to Luzern.
If you are willing to accept hourly bus service, the line from Brunnen along the coast to Küssnacht am Rigi offers quite a few nice towns.
Another thought is the Brunig line. Sarnen has three trains per hour to Luzern, as does Sachseln. Sachseln is on the Sarnersee, with nice views of Pilatus. Sachseln does have a fair amount of traffic from pilgrims to the the home of Bruder Klaus at Flüeli-Ranft.....And, you can go the other way, toward Brienz. Some of the places in the Haslital deserve some time. Depends a bit on how much hiking you want to do.
Good luck finding a place. It is hard to beat the complete set of amenities that Brunnen is blessed with.