The Eau Gallie Arts District has for many years been the home of the Foosaner Art Museum and Art Education Center. The Foosaner Museum is run by the Florida Institute of Technology, and, while small, always has something worth seeing. There is usually one large exhibit occupying the main gallery spaces (although sometimes there are two smaller exhibits), and then there is frequently an associated hands-on activity in another room.
For instance, once several years ago there was a really cool Pop-Art Exhibit, and the activity room, in addition to holding related art from the collection, contained a photo booth. The signal would go off, you would make faces with your loved one, and soon in your email came a digital reminder of your trip. (Unbeknownst to us, as we made our faces at the camera, we were being projected onto the large main wall of the museum hallway).
Make sure to check that the museum is open before you go – sometimes it is closed during normal hours to change exhibits – although, if you do find the museum closed, that’s as good a reason as any to pop into the galleries in Eau Gallie.
UPDATE: Sadly, the Foosaner will be closing its doors permanently June 2021. Brevard is wonderful in many ways, but it definitely needs more art museums. Goodbye, Foosaner! You will be missed.