You can leave Incheon Airport without a visa during your layover if you meet the following requirements. This official site, unfortunately, is quite broken; look up Tourist/Transit (General) (B-2-1) after switching to English:
Visa is a fundamental requirement to enter the Republic of Korea, and in principle, foreigners must have valid visas when they travel. However, those who fall under any of the following categories below are allowed to enter Korea without visas. (Article 7(2) of the Immigration Act)
At this point, click Tourists in transit to Third Countries and find:
Citizens of all countries except Cuba, Macedonia, Syria, Sudan, and Iran.
You transit through Korea on your way to the United States (excluding Guam and Saipan), Japan, Canada, Australia, and New Zealand and hold a valid visa (including re-entry permit, but excluding Japanese Group visa and electronic visa) issued by the aforementioned countries.
You transit through Korea on your way to a third country or the country of nationality via direct flight from the United States, Japan, Canada, Australia, and New Zealand to Korea after legally staying in these respective countries.
Condition of Permission
You have flight tickets that are scheduled to depart Korea within 30 days, and have never overstayed or violated laws after entering countries such as the United States, Japan, Canada, Australia, and New Zealand.
The important one for you here will be that the flight you disembark in Seoul on your return trip must have originated in one of the five listed countries (United States, Japan, Canada, Australia, and New Zealand). For instance, a direct flight from LAX-ICN would be OK since it arrives from the United States, LAX-NRT-ICN would be OK since it arrives from Japan, but LAX-HKG-ICN would not be OK, since that flight would have come from Hong Kong.