This list owes a heavy debt to Katie's guide. I usually rent a little Air BnB apartment in Hongdae, and am quite lazy, so as you can see there's a heavy bias to that university area; no encyclopaedic aspirations here, I'm afraid.
Apartamento (Garusogil), pictured below—they've amusingly (how do Korean businesses get away with this?) ripped off the logo and name from the magazine, but offer solid Italian food, good atmosphere and Bellinis.
Beale Street (Hongdae)—The dry and wet racks of ribs are both excellent, but skip the bacon tasting. If only they'd play Elvis...
Burger B (Hongdae)—great burgers, fish and chips.
Café Sukkara (Hongdae)—warm, wholesome and worth it every time for the shandies and homemade ginger ale.
Chikalicious (Hongdae)—I stumbled across this offshoot of the apparently well-known New York dessert bar and must have looked very excited, because the owner gave me a free sampling. Their Meyer lemon cupcakes are the among the best I've had anywhere.
Coffee Lab (Hongdae)—this is a realistic review; not being a purist, I am crazy for their iced caramel latte.
Coffee K Bar (Apgujeong)—exemplary $20 mojitos that ruin all other mojitos along with your bank account.
Customellow (Hongdae)—Tim had his wedding suit made here and finds it impossible to visit Seoul without buying something every time we visit—most recently: a fox tie. Great with a hot grandpa cardigan.
Design square (Hongdae)—fun design knick-knacks and stationery.
Et M'amie (Hongdae)—raspberry ade and a nice Korean riff on tarte tatin.
Fell + Cole (Apgujeong)—I haven't been to this ice-cream shop yet, but I've subscribed to their Facebook feed and am now tortured daily by the flavors on offer (grapefruit champagne!).
Kamome (Hongdae)—hearty roasted salmon and kimchi tuna onigiri. There's another location near the embassies outside Itaewon.
La Bocca (Itaewon)—attentive service, wonderful yogurt gelato and an impeccable brunch with lace-like hash browns layered with poached eggs, smoked salmon and caviar.
Maad studio (Hongdae)—Tim had his ring re-sized here; great workmanship.
Magpie Brewing Co. (Itaewon)—This modern jewel-box brewery is hidden along a side-street. We sat on the bench outside and enjoyed the cool night air with a Beach House soundtrack.
Molly's Pops (Hongdae)—smooth ice-cream on a stick; some flavours are iffy, I stick with grapefruit, mango and pistachio.
Mui Mui (Apgujeong)—an immaculately modern setting for grapefruit makgeolli.
OK2 Kitchen (Itaewon)—we went here for our wedding dinner; beautiful experimental food, charming service, and the set lunch menus are a steal. For a perfect Seoul day, eat here after visiting the Leeum Samsung museum.
Paul & Paulina's—the flakiest croissants, the crustiest baguettes, this bakery makes everything the —iest, but irritatingly doesn't open until noon.
Platform place (Hongdae)—Nicely laid-out menswear shop with a good casual shoe selection.
Publique bakery (Hongdae)—chocolate éclairs, pistachio éclairs, coffee éclairs...go here for the éclairs.
Sootbul Kalbi (Hongdae)—great Korean barbecue served up by delightfully meddlesome ajummas. The steamed kimchi dumplings from the shop a few doors up are a good cheap fix as well.
Millimeter Milligram (Itaewon)—Great cards, notebooks and strange posters by the delightfully Korean brand Circus boy band (tagline: 'Circus boy band sings underground and plays the various colors').