I live close to Asia Town, so am able to frequent the big three Asian grocery stores in Cleveland (Park to Shop, Asia Food Company and Tink Holl), but making the pilgrimage out to CAM is well worth the trip. This super is BIG, well organized and c l e a n, unlike many other ethnic groceries in the area. Other perks are that there's no smell of fish when you walk in (I'm looking at you, Tink Holl), their prices are reasonable, the employees speak English (unlike Park to Shop) and I can find many different items here than in the others downtown (hello, Filipino ice cream!). The prepared foods section and cafe are a bonus, as well.
A visit to CAM is well worth the trip, no matter which part of town you're coming from!