Roaring Camp - Steam trains from the forest to the Santa Cruz beach (or around the mountains), live country music, BBQ, handcar races, free engineer's hats for dad and hiking.
Michael's Arts & Crafts has a number of father's day craft activities:
June 15 - make a duct tape wallet (6-8 pm) - free
June 16 - t-shirt/tie make it - take it (10-3) - free with purchase of t-shirt or tie
Dad gets a free yogurt at TCBY on Father's Day.
Arrrgghhhh! Talk like a pirate at the Northern California Pirate Festival in Vallejo next Saturday and Sunday.
San Mateo County Fair - Father's Day is the last day!
Visit a museum.
-California Academy of Sciences - Check out their new earthquake exhibit.
-Family Sunday at SFMOMA 11-3 with a family tour at 1:00 - kids get in free.
-Drop-in art at the Jewish Contemporary Museum from 1-3. You'll make 3-D story cubes
USS Hornet -meet WWII vets and hear their stories.
North Beach Festival - Saturday and Sunday from 10-6
Hidden Villa - Banana Slug Band. On Father's Day. Or go the day before and make ice cream with the kids!
Juneteenth Festival in SF- lectures, family art activity, workshops and performances - June 17 from noon to 5. Free
Lots more events. Check the list at SFKids.org, Red Tricycle and Savvy Cities.