If you want to witness what architecture is about, visit SCI-Arc. This is where I went to school ,and I can tell you there is not one day that you will not be surprise what goes on inside this school. From open to the public lectures every wednesday to galleries and installation, and not to mention the student work.
I hang around on the rooftop to relax. Los Angeles traffic is crazy so this is a good place to calm down and try to find my zen. The view is great and I love the rooftop Neon signs you can see from here.
The LA Opera at the Dorothy Chandler Pavilion on Grand Street in downtown LA is a must during the fall and holiday season when they have a solid lineup of opera and ballet. Very inspiring.
It's site says it's "A Friendly Store For Friendly People," and this is completely true. They throw fun parties in the back, and have a sick collection of clothes, housewares, and other goodies.