Updated post with other free events.
So I recently went digging to find out if there were museum fee free days in and around Santa Barbara. Here is what I found:
Santa Barbara Museum of Art free Thursday evenings (5-8)
Santa Barbara Natural History Museum 3rd Sunday (except May-August)
These museums are always free or donation based:
Santa Barbara Historical Museum
Carpinteria Valley Historical Museum
Carriage and Western Art Museum
Hans Christian Andersen Museum (Solvang)
South Coast Railway Museum (Goleta)
UCSB Art Design and Architecture Museum
Westmont Ridley-Tree Museum of Art
Also if you are checking out freebees, look in to the free summer bowling program at Zodo's. http://www.zodos.com/open-bowling/kids-bowl-free-summer/
Please comment with additions and I will update the list!