Shopping?
Hard to say since there are places to shop everywhere depending on what area your going to be in.
LA is huge.
For trendy, open air shopping where you might see some famous people head over to Santa Monica.
There you will want to visit the "3rd Street Promanade" near the Santa Monica peir.
Prices are a little on the expensive side but its a great place to people watch.
After a couple hours or so there,
Head over to Venice Beach.
The Boardwalk is world famous and you wont regret spending a good two hours there having lunch.
Hollywood,
lame.
Its a tourist trap, shopping, well, everything is made in China.
Think the most tacky crap you can imagine then multiply it by ten.
Everyone has to go once especialy if they may never return to LA.
There is also Melrose ave in West LA.
Melrose is also world famous as are the shops.
Again, some shops are very pricy while others are resonable.
I have seen Brad Pitt a few times at the "Johnny Rockets" (a burger place) on Melrose.
Downtown LA has a few areas that have amazing prices on cloths but I havent been there in ten years.
Its also the type of area you can get lost in very easily, its also the type of area you dont want to get lost in, heh.
Burbank has the "Wilsons Leather Outlet".
Think $400.00 leather jackets starting at $25.00!
I have about 20 leather jackets, all from Wilsons Outlet, one had a $600.00 price tag on it but cost me $50.00!
Its a hit and miss shopping experiance though.
I have seen days where their has been total crap on the hangers and the place is H U G E !
You can hit Santa Monica, then Venice Beach, over to Melrose and onto Hollywood Blvd in one afternoon but I suggest going to Hollywood at night. The place looks much better while the lights are on. In daylight, its filthy and full of homeless people.
The shops in Downtown LA and Wilsons Leather Outlet will all close by 6:00 pm.
Those are all areas that are generaly safe for an out of towner where you might see someone famous, alot of hot chicks and also have many areas to take pictures of landmarks to show people for years to come.
The best "tour" of Hollywood is "GraveLine Tours".
Its exactly what it says, it tours sites where famous people have died. It also takes you all around Hollywood including Hollywood Hills.
Well worth the price but you will have to book since they are always sold out. Do a net serach for "Graveline Tours".
Thats about it from me.
I grew up here in LA so dont get lost and end up in a bad area.