Turkey Head
If ya have 7 hours in LA, then do yaself a favour and head to either Venice Beach, or Santa Monica, it is 30-45mins in a cab (about $40 odd dollars) or you can get an Aiport Shuttle for about $15. 7 hours will cut it fine, but none the less....
Visit Library Alehouse in Venice Beach, it is a great pub with a large beer selection. About 30 on tap, alot of belgians and great micros.
Fathers Office in santa Monica is also fantastic, but it doesnt open till 5pm. About 50 on tap, and not a bud or millers to be seen.
Third street promenade is a nice place to pass the time in Santa Monica, and there is a sportsbar (whose name eludes me right now) that has about 40 beers on tap, including Aroogant Bastard, Stone IPA (I think), Anchor, SNPA, and a hell of alot of other great beers.
I know that Library Alehouse does a "tasting paddle" where ya get to choose any beers in 100mL glasses for about a buck each.
It will be a tight squeeze to do this with only 7 hours, and LAX security as it tends to be, but it is possible.
Your next best bet is to go on HBD or somehting like that, tell people where yer gonna be, and ask for recommendations for great bottle shops, and get to them in the evening after work. Alot of the southers states have "blue laws" that prevent the sale of alcohol on sundays, the source of much swearing for me in stinky Valdosta, Georgia, while enroute from NYC to New Orleans for Mardi Gras one year. Apparently they dont know a man's not a camel.
Have fun, there are bollock loads of great beers in the states, if you are only going for a month or so, you can probably do as I do and drink 5 or six different ones a day, and not try the same beer twice. And after 30 days and 150 odd beers, you will be feeling very unwell, and probably happy to come home to the beer desert of aussie bottle shops!
All the best
Trent