With only 3 hours in LA, there's barely enough time to get out of downtown to grab a bite to eat. I agree with most of what JohnE has recommended. I'd give Tito's a pass, they are popular, but the food is ok at best. Phillipe's is just south of Chinatown and near Union station, so you could take the metro there and walk around. It's been voted best French dip sandwiches in LA, and their pastrami and other sandwiches are pretty good too.

The Pantry is also another LA landmark, but if I'm in downtown during the day I skip it and head straight for Grand Central Market in Downtown LA. It's kinda like an indoor farmers market with food and fruit stands. Head straight for the center of it and look for the crowd around the mexican food place. That's where you want to eat. If you have trouble finding it, it's right at the base of Angels landing, the worlds shortest railway.

Of course, the other LA landmarks that can't be missed is Pink's Hotdogs and Tommy's Burgers. Both are open 24 hours if you feel like a late night snack. Tommys is in a bit of a sketchy neighborhood, but if you don't wander around too far late at night it's fine

For shopping there's almost anything you could ever want, but it's probably not close by. If you want a day of shopping you could always head over to Glendale where they just opened up the Americana, a outdoor urban shopping complex which is almost identical to The Grove, plus you can always walk over to the Glendale Galleria which is one of the larger indoor malls in the area. And if you're in Glendale, that opens up a world of options for eating. You almost have to stop by Porto's bakery, I would say that might even be a priority over almost anything else.

You almost have to rent a car in LA, there is public transportation but because everything is spread out it isn't as convienent as driving.