Great Coffee in LA?
I second DanaB's recs. LA Mill is a holy temple to coffee. I've had a lot of coffee from a lot of high-end purveyors and LA Mill serves the best coffee I've ever had in my life. Kenyan AA is my favorite varietal and their version was PERFECT. You'll pay for it but it's truly divine.
Intelligentsia makes wonderful wonderful coffee, too. It's not quite as good in my opinion but it's damn fine and there is much less fuss. It's a cafe where LA Mill is more a coffee-centric restaurant.
If you need to get some coffee a little closer to LAX then I'll add Caffe Luxxe to the mix. They are as good as Intelligentsia but they don't really do american-style brewed coffee much, only having recently added frech-pressed coffee to the menu. They do beautiful espresso based drinks though and they get their pastries from Breadbar.
925 Montana Ave, Santa Monica, CA 90403
Another place that rarely gets talked up here (probably because it's still fairly new) is West Burton Coffee & Tea in Westwood. They don't actually do brewed coffee there, just espresso and tea, but their espresso is definitely on par with Luxxe or Intelligentsia. They're in Westwood Village on Glendon Ave. north of Wilshire.
If you want brewed coffee, though, head to Intelligentsia or LA Mill since they have the mighty Clover.