I was in southern CA for the past few weeks and I made time to visit the Petersen Museum in Los Angeles. For a limited time they are offering something they call "Vault Tours" which are group tours that bring you down into the museum's car storage area.
I mention this only because in the collection, when I went, was a beautiful red Toyota 2000GT.
No other J-tin to speak of unless you are a fan of classic motorcycles. I'm not, but some of the guys in my group were giddy to see some of the rare, old Honda/Yamaha/Kawasaki's etc. in the collection.
I thought the tour was amazing and well worth taking. You get to see probably 200-ish ultra-rare sports cars, movie cars, historic vehicles, one-offs, motorcycles, from every vintage.
Unfortunately there are some things you should be aware of. The tour costs $25 on top of the museum fee. It only lasts about an hour and you have to stay in a group (no rushing ahead or lagging behind). There really is not much time to spend with each car. The cars in the vault are subject to change, so there is no guarantee that the Toyota 2000GT I saw (or any of the cars I saw) are still there. The other disappointment is that you can't take pictures.
It sounds like too many restrictions, but I'm glad I went. There are cars in the collection that I'm sure I'll never see in my lifetime no matter how hard I were to try.
http://www.petersen.org/ is the website for more info.