Try visiting a museum or a new exhibit that you haven't been to. These cultural institutions are a great way to spend an afternoon — you'll be learning more about history and the quiet environment can also be calming. Drag someone along with you for an engaging conversation after your museum exploration.
If you've been to all the major museums in your area, try digging around for some of the lesser known, but equally intriguing ones. For example, in Chicago I remember spotting a hologram museum and a medical devices museum when I was researching tourist sites.
Save Your Bucks: Check the museum websites or call to see what discounts are available. Most museums have certain days in which the public can enter for free or pay discounted admission so be sure to mark those dates on your calendar. To make things easier, just Google your city and the keyword "museum discounts," and you'll find lists that will detail ways you can save on museum outings.
Truly Frugal: There are museums out there that have no admission costs, so those would be great choices for frugalistas.
Source: Flickr User m.a.r.c.