Hello Dillon$$2077
Renting a car while taking trains to explore the mountains is the most expensive way to travel in Switzerland; you will literally waste your money.
My parents are 72 and 82, both have their walking issues; they do not have a car any more, but guess what, they are using public transportation every day, for grocery shopping, excursions, meeting with friends and family, etc. My mum often says, that they can be so lucky to live in a country, where they are absolutely independent thanks to this excellent public transit. To make the story short, taking the public transport in Switzerland for seniors is definitely a no-brainer.
On one hand, renting a car means, you will pay for the car, the gas (which is quite costly here), the parking (in Lucerne, 6 hours parking costs CHF 24), and possibly for speeding, as our roads are equipped with speed cameras; the government is thankful for any unsolicited donation. Cities fight against private traffic and do everything to keep the cars out of their cities. In many cities, you therefore get free transportation by bus & train within the city if you stay at one of their hotels.
On the other hand, many of the locations you are mentioning above are not accessible by car, you will be forced to take the train or any other sort of public transportation as there is no other way to get access to these locations otherwise. Having the Swiss Half Fare Card will make these trips affordable. The same Swiss Half Fare Card you could use for your trips between the cities; it will cut the travel cost for public transportation by 50 %.
https://www.sbb.ch/de/billette-angebote/billette/gaeste-ausland/swiss-halffare-card.html
In addition, having a Saver Day Pass, you can use from as little as CHF 29 the entire Swiss public transportation, and even some mountain trains.
https://www.sbb.ch/en/tickets-offers/tickets/day-passes/saver-day-pass.html
I encourage you to take the trains, as most tourists do here. As I am dealing with tourists for several years, I know that it sounds unbelievable and impossible to someone who comes from a country where the car is the only reliable way of transportation. While public transportation in our country looks rather like a big suburban network, just as they exist in cities like New York, London, or Sidney.
You should at least compare costs and create a spreadsheet. We gladly assist you.
Kind regards,
Roland