Almost all museums/zoos/etc offer a discount for retired people, usually only a few francs, but it's something. There isn't really a comprehensive list, but if there is a place you have in mind, check their website and look for prices with "AHV" discount (AHV is the pension system) - women must be 64+, men 65+. This may be listed under "Concessions" in English. Many art museums also offer certain hours when entry is free, which you can also see on their websites. Theaters/opera also usually offer senior discounts on certain shows.
One of the main benefits of having the Swiss Travel Pass as a lot of museums are included in the price. Otherwise, the overnight guest cards you receive in certain destinations also usually offer discounts on local attractions.