Hello! I would like to search for some expert advice here!

I will be transiting in Incheon, South Korea from 5.50am to 3pm, about 9 hours. Since its early morning, shops probably do not open that early because I have to get back to the airport by 1pm. I was thinking of going to Bupyeong, Incheon, around 1 hour subway ride each way from the airport. There is an underground shopping area there but I was wondering if I should stay in the airport to bathe and use the Internet instead because the shopping time would be around 7 to 12 only, that's not long considering that I have to prepare to leave the place at about 11.30 (if I can't find my way back to the subway station) while the shops only opens at 10am. Would it be more time saving if I just stay in the airport or you guys have more suggestions for visit? Please help! Thank you!