August, if you want to meet lots and lots of people.
September after Labor Day, if you want to avoid the crowds.
April, if you want to see wildflowers and green hills. (We call it "golden", but after May or so the wild oats die and turn brown.)

How long would it take to drive the length of California?
MapQuest says it is 850 miles from Crescent City to San Diego, and would take 14 hours, 9 minutes. I think they are optimistic. Figure two days if you don’t stop much more than gas, food and bathroom breaks along the way, two weeks if you have the time and money. They have you take US 101. California State highway 1 is world-famous; the portion through Big Sur regularly places in the "10 most scenic highways in the USA". It is much slower, though.

What are good places to stop at along the way?
Southern California has the best surfing. The further south you go the warmer the water and gentler the slope. In Mendocino County, for instance, most of the coastline is cliff.

You might re-consider; fly to San Francisco, take Highway 1 south, skip the northern half.

But, since you asked;

Redwood National Park
Any restaurant in the town of Mendocino; if you are a vegetarian, Raven’s:
http://www.ravensrestaurant.com/

The Anderson Valley wine country in Mendocino County

San Francisco

The Boardwalk at Santa Cruz

Monterey – the Aquarium in particular

"Rocky Point" restaurant, 10 miles south of Carmel
http://www.rocky-point.com/

Hearst Castle
Mission Santa Barbara
Venice Beach

San Diego has a world-famous zoo.

The best time of the year would be right now! Or maybe a day that is a little warmer.

Some stops along the way include:
– Chandler Drive-thru Tree and the One-Log House
– Point Reyes National Seashore

And the length would be about more than 5 hours?