For restaurants, some personal favourites:
The Little Door - on 3rd Street, nice vibe and people and an open air dining room (note no liquor, wine only and a good list)
Koi - wonderfully mouth melting sushi
Dolce - Italian on Melrose, very nice
La Dolce Vita on Santa Monica Blvd - for a bit of old Hollywood
Cut at the Regent Beverly Wilshire is supposed to be one in current fashion / rage - not been yet and will try it in early May
Places really disliked include Mastros - hideously noisy and full of tourists (!!!), and the steak didn't live up to expectation plus bookings are all a mess so lots of waiting at the bar. Spago is good, but again once you get over the noise and busy-ness of it, also the dining room is large and there are nice areas and not so nice areas to eat.
I see you arrive on the 9th, shame, the no. 1 and I will be resident at the Peninsula from the 4th till the 8th. We are also doing the Universal VIP tour so will send any useful tips.
Also agree with others about the Getty centre - the new one not the original (which is a nice drive up the coast but unless you like statues very disappointing on arrival). The new centre itself is amazing and does have great exhibits, especially photography and as mentioned grat views!
Other things not mentioned: I like motoring up to Malibu for lunch by the sea (the Chart House), going up to Hearst Castle (which is a day trip at the very least, so maybe better saved should you ever drive from SF down to LA), Rodeo Drive is a pleasant walk but the Grove is better really for shopping, also like people watching and walking in Venice Beach area ... and yes, open houses are a real fun way to spend a few hours, cruise around Beverly Hills and just drop in!
There's a plane at JFK, to fly you back from far away
all those dark and frantic transatlantic miles