Is there any good shopping centers around the staples center in los angeles?

I will be in LA next month on vacation. I will be staying in Anaheim going to Disneyland. I am very familiar with the Orange County area, but not so much with the LA Downtown Area. I am from the Bay Area. For one day me and my family are planning on going to the Getty Villa, and to go to the Staples Center (to the store, I am a Lakers fan). Then some of my family wants to go shopping. We are trying to figuere out if there are any shopping centers around the staples center. we dont want to go too far away from staples center area. and we have already been to the block at orange, south coast plaza, and the mall that is in fullerton. thank you