Hey everyone, I just booked my flights with Korean Air! It ended up being more than $500 cheaper since Qantas went up

But I have another query - my return leg (LAX-SYD) looks like this:
[TABLE="class: tableFlightConf"]
[TR]
[TH="colspan: 3"]Los Angeles to Seoul [/TH]
[/TR]
[TR]
[TD="class: space"][/TD]
[TD="class: space"][/TD]
[TD="class: space"][/TD]
[/TR]
[TR]
[TD="class: textBold flight"]Flight 1[/TD]
[TD="class: textBold, width: 83%, colspan: 2"] Wednesday, July 18, 2012 [/TD]
[/TR]
[TR]
[TD="class: textColorBold"]
[/TD]
[TD="colspan: 2"] [TABLE="width: 100%"]
[TR]
[TD="colspan: 3"] [TABLE="width: 100%"]
[TR]
[TD="class: textBold, width: 15%"]Departure:[/TD]
[TD="class: nowrap"]23:30[/TD]
[TD="width: 90%"] Los Angeles, USA - Los Angeles International, terminal B [/TD]
[/TR]
[TR]
[TD="class: textBold"]Arrival:[/TD]
[TD="class: nowrap"]03:50 +2 day(s) [/TD]
[TD] Seoul, Korea (Republic of) - Incheon International [/TD]
[/TR]
[/TABLE]
[/TD]
[/TR]
[TR]
[TD="class: space, colspan: 4"][/TD]
[/TR]
[TR]
[TD="class: textBoldSmallFlight, width: 15%"] Airline: [/TD]
[TD="width: 35%"] Korean Air KE012 [/TD]
[TD="width: 50%, colspan: 2"] [TABLE="width: 100%"]
[TR]
[TD="class: textBoldSmallFlight, width: 29%"]Aircraft:[/TD]
[TD] Boeing 747-400 [/TD]
[/TR]
[/TABLE]
[/TD]
[/TR]
[TR]
[TD][/TD]
[TD]
[/TD]
[/TR]
[TR]
[/TR]
[/TABLE]
[/TD]
[/TR]
[TR]
[TD][/TD]
[TD="class: space, colspan: 2"] [/TD]
[/TR]
[/TABLE]
[TABLE="class: tableFlightConf"]
[TR]
[TH="colspan: 3"] Seoul to Sydney [/TH]
[/TR]
[TR]
[TD="class: space"][/TD]
[TD="class: space"][/TD]
[TD="class: space"][/TD]
[/TR]
[TR]
[TD="class: textBold flight"]Flight 1[/TD]
[TD="class: textBold, width: 83%, colspan: 2"] Friday, July 20, 2012 [/TD]
[/TR]
[TR]
[TD="class: textColorBold"]
[/TD]
[TD="colspan: 2"] [TABLE="width: 100%"]
[TR]
[TD="colspan: 3"] [TABLE="width: 100%"]
[TR]
[TD="class: textBold, width: 15%"]Departure:[/TD]
[TD="class: nowrap"]19:10[/TD]
[TD="width: 90%"] Seoul, Korea (Republic of) - Incheon International [/TD]
[/TR]
[TR]
[TD="class: textBold"]Arrival:[/TD]
[TD="class: nowrap"]06:25 +1 day(s) [/TD]
[TD] Sydney, Australia - Kingsford Smith, terminal 1 [/TD]
[/TR]
[/TABLE]
[/TD]
[/TR]
[TR]
[TD="class: space, colspan: 4"][/TD]
[/TR]
[TR]
[TD="class: textBoldSmallFlight, width: 15%"] Airline: [/TD]
[TD="width: 35%"] Korean Air KE121 [/TD]
[TD="width: 50%, colspan: 2"] [TABLE="width: 100%"]
[TR]
[TD="class: textBoldSmallFlight, width: 29%"]Aircraft:[/TD]
[TD] Boeing 777-200/200ER [/TD]
[/TR]
[/TABLE]
[/TD]
[/TR]
[TR]
[TD][/TD]
[TD]
[/TD]
[/TR]
[TR]
[/TR]
[/TABLE]
[/TD]
[/TR]
[/TABLE]
I arrive in Seoul at 3.50am, and depart the same day at 7.10pm. Will there be hotels open at this time? Or is it alright to sleep in the airport, and then put my luggage somewhere and walk around Seoul for a bit?