행복이 가득한 집 (The House Filled with Happiness or more commonly known as the Happy House) is a 1930's Japanese colonial house transformed into a semi-luxurious restaurant cafe.
Information on the Internet is difficult to come by and so far all I've found is this review that talks about both the cafe and the neighbouring Mokpo Modern History Museum. The review is entirely in Korean, but it does have this useful line of information:
행복이 가득한 집 061-247-5887, 11:00~24:00, 차 5000원대, 식사 1만원대Which roughly translates out to this:
Phone: 061-247-5887The food is an average mixed of western and Korean dishes, but most of the foreigners in Mokpo really dig the place for its cafe decor and its five dollar shakes.
Hours: 11:00 to 24:00
Prices: Tea 5000W & Meal 10000W