Visiting LA from SF....
I would agree with Franklin Jefferson's recommendations especially Palate. Fraiche also comes to mind for wonderful French food. For Italian you might want to try Angelini Osteria or La Terza. Hungry Cat is a wonderful place for a more casual/people watching in Hollywood. Another option in a cool area is Abbott Kinney in Venice. I have heard wonderful things about Gjelina and AK restaurant+bar.
Fraiche, or Josie's market menu... but honestly, if you're visiting from SF you're just going to shake your head and say, "huh, better at home". Indulge in what we do best -- Korean, Thai, sushi, Mexican, Vietnamese, or head out to the SGV for Chinese that will make you forget SF Chinatown.
And do tell us where you're staying -- if you're staying in Santa Monica, recommendations for Pasadena are useless.
You'd do very well at any of Neal Fraser's or Suzanne Goin's places (Grace, BLD, Lucques, AOC, Hungry Cat) for similar food. But since the places you mention are all basically in the Mission (I think, been a while since I was home), you might want to try some of the places in the SilverLake or Atwater Village area for a similar vibe. Any other Hounds have some suggestions for that kinda grub in those neighborhoods? Palate's the only place that readily comes to mind.
Canele in Atwater Village is supposed to be great, and inexpensive!
But I agree with Das Ubergeek - instead of trying to find similar places, why not try what LA does best? (i.e. our ethnic foods) If you like Korean soon tofu, try Beverly Soon Tofu on Olympic.
Vietnamese is best in the Westminster area but that's getting into OC and since we don't know where you're staying, that might be too far?