We've never actually tried the sushi from Sushi Gallery on Payneham Road (if you want sushi, you'll need to pre-order or go for lunch), but every dish we've ever eaten there has been fantastic. This little gem of a cafe is run by a Korean family who really care about the quality of the food they serve.
On a busy night you may have to wait up to 45 mins for your food to arrive, but you will be rewarded with a delicious, affordable and satisfying meal. Food comes with complimentary cold water and kimchi (pickled vegetables w/chili). The Bulgogi Donburi (front $10.90) & Japche (back $13.50) are pictured below. The noodles in the Japche are made of sweet potato...refreshingly different.
One of the better known Korean dishes is the Bibimbap. It's a bowl of white rice with sliced veggies and usually sliced beef and a fresh or fried egg on top. The Bibimbap at Sushi Gallery is the best we've tried. Here's one that comes in a hot stone pot, the Dolsot Bibimbap ($12.50).
Another recommended dish is the Ttukbaegi Bulgogi ($12.50) which I'm still trying to learn how to pronounce. It's seasoned beef with Korean sweet potato noodle and vegetables in a hot pot.
Yet another option is a Chicken, Pork or Fish Katsu ($11.50). From what I can tell, this is a Korean take on Western fried foods. Very tasty!
For dessert, I recommend a trip across the road to the Lucky Mart Korean shop for an ice cream or packaged dessert. (note: they close at 8pm) We usually go for the Melona ice cream but we recently tried the Corn ice cream and it was both strange and awesome at the same time!
Sushi Gallery for lunch or dinner (closed Sun) and Lucky Mart for dessert makes for an awesome Adelaide Korean meal combo.
Update 5 Feb 2012:
We've been back to Sushi Gallery a couple of times recently to try the sushi at lunch. It's the best sushi I've had in Adelaide and made fresh after you order. Delicious! A must try for all sushi lovers.
Avocado Shrimp Roll ($9.50)
Teriyaki Chicken Roll ($6.90)