I used to love Seoul Restaurant (first place my son ate at a resto!), but they've changed hands, so I can't vouch for them any more.
If you want to venture a few blocks east into the Annex, there is New Generation Grill House (just west of the cinema, right across the street from Lee's Palace). That's where they do the BBQ hole in the middle of the table ( with ALL YOU CAN EAT MEAT! Don't bring the vegetarians), and grill the prepared meat yourself as it arrives. Even if you've been to other such restaurants, this is by far the nicest in the city. The music is still lousy, but the decor is a mix of stylish and adorable, the washrooms impeccable, and the service much friendlier than most. Oh, and they're cheap, including the beers. Perfection.
Two of us went to "Song Cook's Corean Chilli" just west of the Korean supermarket at 681 Bloor last Monday evening. We had pork bone soup and spicey sweet chicken both very good and more than enough for two. Service was very friendly, all the other diners appeared to be Korean. Total cost including tip $30. Your daughter might be entertained by the pop videos playing on the walls as well.
However, I too am ignorant about Korean food and what is best in that 'Korea Town' strip. I would like to hear an answer to your question from someone with more knowledge than myself!
If it's your first time trying Korean food, I'd say a good place to start would be Korean Village restaurant (628 bloor? - stone exterior, yellow sign with red chinese characters on signage) - this is one that's been around for a very long time. the menu offers a range of classic/typical, solid korean dishes, a good variety of side dishes and the prices are fair. I'd also recommend Il Bun Ji which tries to emphasize its Japanese menu but it's korean owned and their Korean menu, tho not extensive, is good. On the Bloor/Christie strip, I'd put these at the higher end in terms of quality of food & atmo.
My second tier choices would be Jin Mi Rak or Korea House, food is good and prices may be a bit lower than the first two mentioned. Both offer a broad range of items.
In the third category, I'd place the specialty places like Joon's, Buk Chang Dong Soon To Fu (orange building), Owl of Minerva all of which are known for one or two dishes, or specialize in certain dishes; they are also more 'fast food' in style. Buk Chang Dong can't be beat for their stone bowl rice and silky tofu stews which are reasonably priced: they rule this dish in t.o. Many claim that Owl is the place to go for pork bone soup.
If you are a novice to the cuisine, I'd recommend starting out at the 'full' range restos then, once you have a better idea of what you like, check out the other specialty places
il bun ji has seriously gone downhill ... it's now changed its name slightly ... the food is awful ... the bulgoki tastes like boiled beef and the spicy octopus is covered in a mixture of ketchup and tobasco ... i used to love this place - but no longer ... i think it may have actually changed management
I really like Korea House (666 Bloor, I think- on the north side). It's a family run place- not fancy, but always busy with a mix of Korean and non-Korean customers.
Good fresh ingredients. nice side dishes.
I generally have kimchi jegae or bim bim bap, delicious.
Their mandu- dumplings- come in a massive serving size, so be forewarned.