As I life-long resident of Pasadena up until a few months ago (we moved 30 minutes North) I would rate The Luggage Room (at the train station in Pasadena) as my overall favorite in Southern California. Olive wood in the WFO, naturally leavened dough, farm-fresh toppings; it's tough to beat. My favorite pizza there is the "Gladiator" with added green olives and I prefer mine with some char. Their restaurant next door, La Grande Orange is likewise excellent and I've never had a bad meal there. Both places are a great hang. Cool, but not so trendy that you feel out of place.
I would suggest skipping Bella's Gourmet Pizza, Tarantino's as well as Avanti Cafe (which is NOT the best pizza in Pasadena by any measure).
Brothers Pies N Fries off Colorado Blvd in Old Town makes a NJ-ish pizza. The pizza is baked to perfection with a very expensive Cuppone oven, but they only make same-day emergency dough. Ugh.
Casa Bianca in Eagle Rock, the town immediately West, might be of interest. They make a Chicago thin crust, but I'm sad to say that their quality and consistency has fallen off. When they make a good pizza, I would put that near the top of my list of "electric chair request" meals. They're closed on Sunday and Monday. I would suggest going there before 5:40 on a Tuesday or Wednesday (open at 4) otherwise you may experience a very long wait for a table. The rest of the food on their menu isn't memorable with the exception of their Pasta Al Forno.
Masa of Echo Park, about 15 minutes south of Pasadena, makes an excellent Chicago deep dish. It's not my cup of tea, but they do it very well.
Pizzeria Mozza (about 20 minutes south of Pasadena) is a bit pricey, but what sets them apart is the fact that they cure their own meats in-house. If you go there I recommend getting the caprese salad with their garlic bread. It's one of the most memorable things I've ever eaten. It's THAT good. Their regular restaurant next door, Osteria Mozza, is incredible (the mozzarella bar will blow your mind) and it's pricey as well. But if you're celebrating a special occasion it's worthwhile.
Finally, I have to mention Vito's Pizza on La Cieniga (near Beverly Hills, 30-40 minutes away from Pasadena). It is a NJ/NY slice joint that is the equal of any deck oven pizza place back east. Even Scott123 has ogled and admired the photos of their pizza. Vito uses an heirloom yeast (don't call it a sourdough in his presence) that's been in his family for over 100 years. The dough doesn't have an obvious sourdough tang, but it does have a lovely, subtle aroma and taste. It's the simplest pizza of all the one's I've listed, but it's memorable nonetheless.
A couple of other places that deserve a quick mention are Tomato Pie Pizza Joint (in Silver Lake; NY pizza, about 20 minutes south of Pasadena) and Slicetruck Pizzeria in West LA (best American style pizza I've ever had).
If you have questions about any other places, chances are I've tried it. Don't hesitate to give me a shout.