Tlapazola makes amazing margaritas without any artificial mixes-- their top shelf margarita is the best I've had in LA. If you want something lighter, their blended fruit ones are delicious, especially the mango. They also have an excellent menu; food is always fresh and full of flavor. Make sure to order the fish of the day with the yellow mole and lime caper sauce!
11676 Gateway Blvd
Los Angeles, 90064
El Carmen on Third just east of the Beverly Center (on the south side of the street, just next door to the Little Door) makes a damn fine Margarita. They probably have a mix if you don't ask, but they have one of the best tequila selections in town, and will make them from scratch if you ask. They also have a divine fresh pineapple/white tequila mix going on the counter; it's like $7 per shot, but it's very tasty.
I can't speak from experience, but I would speculate that you could get a well-prepared margarita from the Hungry Cat, too, since they use all fresh juices in all their other drinks. Hungry Cat is in the little development across the street from the Arclight, on Sunset near Cahuenga.
You may want to ask the bartender if he/she can make fresh lime juice margaritas. Be careful, though--we once had a bartender give us margaritas made with Rose's lime juice--just awful. Some bartenders have a special lime squeezer thingamajiggy, so it's not so hard to squeeze a few limes over some ice and tequila, and add some Triple Sec. Sometimes the bartender will do exactly what you want, sometimes the bartender will try but will do it all wrong, and more often than not the bartender will look at you like you're crazy. Good luck!
I'm a bartender and I never look at a guest as if they are crazy. Unless they're mean, then I will do that. But if you were to say, "man, could you make that fresh?"
I do it, especially since I work in a place where drinks are eight bucks.
The other day I made a whiskey sour with fresh lemon juice and I thanked the gentleman for the opportunity to make it.
Why is it so hard to find a real Margarita? Anyway, the best I've found, most already mentioned:
I agree with Deana's comments. Any competent bartender should willing to make a margarita without the nasty, sugary mix. That is unless the management frowns upon such actions.
I also agree with DanaB's suggestion of Hungry Cat. They use fresh-squeezed juice in all of their cocktails. Bound to be good.