Best free things to do in Bakersfield?

The Kern River. You can see beauty from Hart Memorial Park. They have a small lake you can rent paddle boats and cruise the lake and feed the ducks and see peacocks and other wildlife. 
The Kern Canyon - many beautiful sights , the Kern river runs along side the canyon. 
Do NOT enter the river waters by any means. The current is extremely dangerous and fast flowing. But very beautiful to see.

California Living Museum, Kern County Museum, Buena Vista Museum of Natural History & Science, Bakersfield Museum of Art

Kern County Museum may have a small entry fee.

You can feed the peacocks at Hart Memorial Park. Not much free things to do here. California Living Museum is a small zoo you can visit. The park at river walk is a nice park with bike trails . There is Murray Family Farms Where you pick strawberries, pumpkins or buy from the shop inside where they have lots of fresh fruit. And there's river rafting.