If you just want to soak up local flavor you are already In the right place. Walk around the Venice canals. Mapped at link below
http://www.downtownculvercity.com/dine.html
Gorgeous photo: http://www.hillhaus.com/photos/2007.03.19.Los.Angeles/16.Venice.Canals.jpg
Read the history of how the canals came to be. Walk along the canals, bring some breadcrumbs for the ducks.
Then there is the freaky Venice beach boardwalk, and muscle beach (great photos for you guys on the rings or ropes?).
Some major people watching.
Driving around la is the worst part of the city and you are already in a very interesting (though liberal) part of the city with a lot to see and do..
I read a series of books that centers around the Venice canals. Sounds like a great walk with gardens and all as well as close at hand.
