a few suggestions from someone who is from the la area and currently lives in san francisco: sf is a great place for tourists, and much easier to get around in than in la. though you will have a car, so that makes it a bit easier... los angeles and its surrounding cities are fairly spread out. i think a thomas guide of la and orange counties would be a really good investment if you'll be driving around there (
http://www.randmcnally.com/rmc/store...hdghf.0&cmty=0) i just know it's personally indispensable for someone like me, with no sense of direction. some of my favorite things around la (that others have enjoyed visiting):
-the beaches
-disneyland
-the getty museum
-the museum of contemporary art
-the natural history museum and la brea tar pits
-restaurants, clubs, etc. that you might have seen in movies. if you've seen the movie swingers, one of my favorite places to have drinks is the dresden room (where marty & elaine perform).
crime in la? i guess, if you're in bad neighborhoods. but i don't think la is any more unsafe than any other big city. i'd just follow a general rule and say if it feels uncomfortable, don't stay there.
as for san francisco, i have plenty of suggestions as to things to visit here!
regarding the 7 days in las vegas, i've been to vegas before and i think you could do with 2, tops. it's fun if you have money for gambling, food, tourist traps, but gets tiresome fast. i would add most of those days onto another destination.