In the past, I've gotten very good deals on rentals at SFO. Not so much LAX. But, it doesn't hurt to comparison shop that point too. 16 days is a good amount of time. You'll be able to see quite a bit. I thought maybe you were talking about what a lot of people do...the one week fly through the state. Please be aware that if Yosemite is on your list, you will need to reserve lodging and park entrance well in advance. Very very popular tourist attraction and access is limited (the park is being loved to death). But, it is spectacular, and there are some big trees there too. Yosemite has some groves of tall trees. While Sequoia has the largest (heaviest, tend to be a bit shorter) living things in the world. Both are worth seeing. On the coast, I'd rank the Monterrey Bay Aquarium (in Carmel) as worth your time. I also love the area around Big Sur (south of Carmel) as being truly spectacular for scenery. I'm not sure of the "open" status of Highway 1 in that area though.
In the San Francisco area, Muir Woods (30 minutes or so north of San Francisco) has some redwoods worth seeing, but again, a very popular tourist attraction. If you are at all into hiking, my favorite tip is to tell people to park near Mountain Home Inn (on Highway 1 in Mill Valley) and walk into the park. There's a free lot right across from Mt Home Inn, that will usually be vacant or nearly so on a weekday. No entrance fee. Avoid the massive crowds in the parking lots. Beautiful hiking....it's maybe 2 miles down into the park, and then (of course) 2 miles back up to your car. It is not all that difficult of a hike....my husband and I did it many times with our babies in backpacks, so obviously not that strenuous).
The whole coast in Marin is pretty neat, if you follow Highway 1 from Mill Valley, over to Stinson Beach, and on to Point Reyes National Seashore, with it's incredible beaches (North and South beach....not "warm water" beaches by any stretch, but just beautiful and usually vacant). In Point Reyes, the Station House Cafe is an institution, and serves fabulous food.
In the south, continuing from Big Sur, I love Santa Barbara.
HTH. I lived north of San Francisco in Marin for 20 years.
