My wife and I stop here just about weekly for kimchi, laver and rice. The pricing is average and can actually be very good if there is a sale going on. The quality and freshness of the produce, banchan, and other fresh foods is usually top notch and kept in a constant rotation. Occasionally you might get a day old kimbap, but that is extremely rare.
The meat sold here is of good quality, and they sell a lot of cuts not normally found at the grocery store. The seafood department also has a very large and fresh selection of fish. If you looking to save some money, definitely check out the frozen meats as well. Their are a lot of good quality items that are frozen to preserve and then sold at a discounted price. You'd be really surprised at the quality of the frozen meat and fish.
Beyond fresh foods, they stock a multitude of worldly goods from almost all parts of the world. It's really fun just to walk around and find new things to try. I will say though that this location does not specialize in Korean product like the Mesa location does. So if you are looking for something very Korean specific, definitely check out the other location on Dobson and Southern.
I have visited Asiana Market since I was a little boy, and I have plenty of fond memories just wondering aisles and finding new snacks to try. I highly suggest you give it a shot too and expirience something new.