This Asian supermarket is the absolute heart and soul of the Chinese Cultural Center. When I first moved to Phoenix, it took me about 4 months before I ever met ANY other Asian people. It was astonishing to me. Coming from Los Angeles, and being the only Asian person in my classes in Phoenix and having to explain WHERE the Philippines was...just such a foreign thing for me. Anyway, when a friend of mine took me here for the first time, I fell in love. Not only were there a) real Asian people inside, b) everything you would need to make anything from any part of SE Asia, but c) the prices were cheap and the quality was better of most grocery stores in Arizona. Ample free parking and some decent Chinese restaurants next door, this is definitely the place to go closest to downtown Phoenix for all your Asian cuisine needs.
Get the mock duck tofu...it's amazing. I still stayed away from the sashimi grade fresh fish though...you just never know sometimes.