Here are the hotels that you can rent for day use. Day use (대실, dae-sil) means renting a room for couple of hours, as opposed to overnight renting. You can use the room for 3~4 hours, and the cost is about 50,000 won. Unfortunately not all of these places have a website in English. But a map, full address in Hangul and phone number should be able to give you good idea about where it is.
In Gangnam Area
Hotel the designers Samsung
http://map.naver.com/local/siteview.nhn?code=21518477
서울특별시 강남구 테헤란로9길 7 (02-568-8371)
April Hotel
http://map.naver.com/local/siteview.nhn?code=19449251
서울특별시 강남구 언주로89길 13 (02-3452-4900)
Lex Hotel
http://map.naver.com/local/siteview.nhn?code=32769113
서울특별시 강남구 강남대로 588 (02-511-4488)
Noblesse Hotel
http://map.naver.com/local/siteview.nhn?code=10983887
서울특별시 강남구 테헤란로25길 6-13 (02-558-1202)
Sohsul Hotel
http://map.naver.com/local/siteview.nhn?code=35032731
서울특별시 서초구 반포대로14길 53 (02-507-0505)
A Seven Hotel
http://map.naver.com/local/siteview.nhn?code=18769671
서울특별시 서초구 반포대로14길 45 (02-588-2044)
Tria Hotel
http://map.naver.com/local/siteview.nhn?code=12003455
서울특별시 강남구 테헤란로33길 16 (02-553-2471)
In Mapo Area
Hotel the designers Hongdae
http://map.naver.com/local/siteview.nhn?code=31384737
서울특별시 마포구 양화로 86 (02-326-5801)
In Jongro Area
Hotel the designers Jongro
http://map.naver.com/local/siteview.nhn?code=33706031
서울특별시 종로구 수표로 89-8 (02-2267-7474)
In Yongsan Area
In Yeouido Area