Since you'll be in SJ, I suggest SF.
It is about one hour north, without traffic.
Get a hotel on Union Square or Downtown.
You should be able to get around SF on MUNI.
You can get around the Bay area on BART.
You can get a bus to other attractions (Muir Woods).
I've meet people from the East Coast that think LA and SF are neighboring cities.
If you decide on LA, you will need to fly.
Or rent a car, hop on the Bug Bus, ride the train. All three will take most of the day.
If you like the beach, it will not matter.
It is going to be cold, anyway.
Just don't go swimming on Ocean Beach (riptides).
if you go to LA, you'll need to rent a car.
Keep in mind that rush hour SF traffic is a killer grid lock and starts about 2pm.
Not that LA traffic is any better.
Your other local options include Yosemite or Santa Cruz/Monterey.
You may run into snow @ Yosemite, though.
And, I would leave May 6th, since that is a Sunday.
Lived in SF and the Bay Area.
Live in Tarzana (LA).