You might consider staying in Hongdae since there's an Airport train stop there (Hongik Univ). Unless you must stay at Hilton or Marriott. There's a brand new(ish) HIX right there by the train station. Getting around the rest of town is relatively easy via public transport. I stayed at an Airbnb right on top of the station there and felt like it was an OK base for the week I spent using a combo of subway and the commuter trains.
Do you really need to be at the airport 3 hours early? Granted I was flying up front but don't recall arriving more than about 2 hours early. Took the Arex train and arrived in plenty of time. It does take a while though.