There is a small Asian market on US19 in Holiday (I believe). It is on the west side, and the name is Thai Hao. I'm not sure why it is named that, but the owners are Vietnamese.
My wife is from Laos, and we do all of our shopping for asian good down in St. Petersburg. I don't know if you're totally new to Pinellas county or just Northern Pinellas county. There are a ton of asian stores in St. Pete. Let me know if you need names/locations for down there. It is worth the drive.
If you're looking for asian produce, go to the Wagon Wheel flea market on Park Blvd. in Pinellas Park on Saturday or Sunday mornings. Don't go to the inside sections (for the produce), as all the asian (mostly Thai/Lao/Vietnamese) set up in the outdoor area at the far west end of the flea market.
Cho Lon Oriental Market at 5944 34th Street North
Dong A at 26th Street and 30th Avenue North
Dong A (a second one) on 49th St. North I believe at 84th Ave. North.
There are several others in St. Pete as well. Cho Lon is probably the largest asian store in St. Pete. I know there are some in Tampa, but I work in Pinellas Park (live up near Eastlake area south of Tarpon Springs) and all my wife's relatives live in St. Pete. I also end up eating (normally Vietnamese, but sometimes Thai) in St. Pete/Pinellas Park at least twice a week.
Not famliar with that area, but if you strike out we have some killer ones in Tampa...
Some of the bigger ones are:
Oceanic Oriental Supermarket at 1609 North Tampa Street... (favorite)
Din Ho Market at Waters Ave. & Armenia... (tied with MD for second fav)
MD Oriental Market on Fowler Ave near I-275...
Kim Brothers at 4021 W. Hillsborough Ave. near Dale Mabry....
S Mart at 7030 W. Hillsborough Ave. in Town & Country...
Yeah, they all know me....