Quality Seafood is the place on the West side. It's in the Redondo pier complex. I don't know the address, even though I've been a customer for about 30 years. To get there, park in the structure that's between PCH and the highway. When you enter the structure, drive as far back to the opposite side that you entered that you can. There's a stairwell there that goes to the lower level of the structure and the store is there on your right side.
They have large tanks of live crab and lobster along with any kind of fresh anything from the sea that you may wish. They will steam cook your purchase free of charge and they even have tables there that you can use if you want to eat on the spot.
Sometime my wife and I go there on a Sunday and get 5-6 dungness crab and eat them there. It's usually pretty crowded, but that's part of the fun.