Santa Monica isn't that close to LA really so if you want to do the studios, rodeo drive, walk of fame etc I'd stay in LA. Santa Monica is nice for a break from the city but I wouldn't make it my base for the tourist stuff
I wouldn't want to drive in to LA every day, the traffic can be a nightmare, do the busy stuff then have a couple of days to relax. We stayed at shutters on the beach - the most comfortable bed I've ever slept in
re your comment:- "I'd taken a fancy to staying Santa Monica and hiring a car to drive into other parts of the city"
I would personally stay more centrally located (particularly for instance if you want to see Universal and the area around Manns Chinese theatre) and then stay in Santa Monica for a couple of days before further moving on.
LA is not just a series of neighbourhoods. Its a urban sprall where around 18.6 million people live and is made up of around 100 separate cities that merge into each other. How confident a driver are you in 4 /5 lane freeway traffic that can on occasion make the M25 look quiet in comparison?.
What ideally would you like to visit in LA for the days you are there?.
I used to live in SM, shutters is fantastic but expensive. Stay in SM as its safer and nicer that Venice and LA. Do go to Venice, maybe walk or cycle along the boardwalk down to Venice (hire from Perry's on the beach). Take the 10 Freeway after 10am into LA and you'll be fine. Enjoy! It's fabulous!