This is the place where Seonjae and Hyewon went to have breakfast in ep 12 during their trip.
After rewatching Ep 12 last night, I found this place from the clues in the drama, and it is actually quite close to Seorak Myeon (설악면) which is on the way from Seoul to the pension. For details about transport, please check the post about the pension. And when I searched for the street view on daum, there is actually SLA drama pics outside the place!
On the map below, the bus sign on the left hand side is Seorak Myeon Bus Terminal and the place marked with A is the restaurant. It is less than 5 minutes of walking distance.
Address：경기 가평군 설악면 신천중앙로 97