OK, cool restaurant/bar/hangout is The Perch in downtown LA. Nice balcony view from a high rise building.
Alimento is a great restaurant in Silverlake.
Everson Royce is a great wine shop with tastings in Silverlake.
In addition to bsman's Arboretum recommendation (it's the former estate of Lucky Baldwin, early LA landowner, with gardens and the house from Fantasy Island as well as the shooting location for the early b&w Tarzan movies), there is Huntington Library in San Marino and Descanso Gardens in La Canada. They're all know mostly for their gardens, but Huntington Library is the former estate of Henry Huntington with an actual library (for scholars, but a showroom on the ground floor with an original Gutenberg bible, early American writings, etc. all on display), an art gallery (two actually, the one in the original house has Blue Boy and Pinkie, other Gainsboroughs, Turners, Rembrandt, mostly British artists, and the other newer gallery with more diverse offerings). The gardens are beautiful and there are several places to eat on the estate.
The Norton Simon museum in Pasadena is probably the best art museum in LA.
Disney Concert Hall and the Broad Museum are popular tourist destinations and worth seeing. Booking a concert at the Disney Concert Hall is well worth it to enjoy the interior design and acoustics.
Catching any concerts at the Hollywood Bowl is definitely worth it. They have an onsite restaurant and many food outlets to buy gourmet food that you can eat at your seats. The classical concerts are relatively cheap.
I would recommend Santa Monica over Venice (Venice is entertaining, but it's like the inner city on the edge of the beach). Pasadena has a great Old Town where you can stroll, shop, and go to restaurants (convenient if you go to Norton Simon, The Huntington, or the Arboretum). If you go to the Arboretum then I would recommend eating at a dim sum restaurant in the Arcadia mall (just across the road, it's now called Westfield Arcadia mall). The restaurant is Din Tai Fung and is hugely popular, there is always a line but they move people in and out at a good pace.
I wholeheartedly agree with Getty Villa (lots of ancient Greek artifacts and a beautiful spot near the ocean) and Griffith Observatory. Malibu is nice and has some great hiking trails, esp near the creek. A lot of the beach along Malibu is private access only, so the easier spots to get to are Zuma Beach and Pt. Dume. Location for lots of movies and shows.
San Pedro is a little dull, but close to the ocean and doing the PV (Palos Verdes) loop is a nice drive. It's the site of the former Mainland, which doesn't exist anymore. You'll see tons of seals on the coast though. Neighboring Torrance is one of the oldest Japanese communities in LA, so there are a few good Japanese restaurants around there. But if you want the best sushi in LA you'll have to drive to Studio City, on the other side of the Hollywood Hills (north of), near Universal Studios. So if you go to Universal and you like sushi, gotta go to Ventura Blvd in Studio City. Sushi Katsu-Ya is the one to try. Also very popular so there might be a wait.
Upper Sunset Boulevard is a nice drive and site seeing spot. Don't assume every restaurant on a famous street is good though.
