You are a US Green Card holder and a South Korean citizen. Frankly, your citizen gives you more travel privileges than the Green Card. Per wikipedia these are the countries which offer visa-free or visa-upon-arrival travel to South Koreans and/or Green Card holders:
Albania, Andorra, Antigua and Barbuda, Argentina, Armenia, Austria, Bahamas, Bahrain, Bangladesh, Barbados, Belgium, Belize, Bermuda, Bolivia, Bosnia and Herzegovina, Botswana, Brazil, Brunei, Bulgaria, Burundi, Cambodia, Canada, Cape Verde, Caribbean Netherlands, Cayman Island, Chile, Colombia, Comoros, Costa Rica, Croatia, Cyprus, Czech Republic, Denmark, Djibouti, Dominica, Dominican Republic, Ecuador, Egypt, El Salvador, Estonia, Ethiopia, Fiji, Finland, France and territories, Gambia, Georgia, Germany, Greece, Grenada, Guatemala, Guinea-Bissau, Guyana, Haiti, Honduras, Hungary, Iceland, India, Indonesia, Iran, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kazakhstan, Kenya, Kiribati, Kuwait, Kyrgyzstan, Laos, Latvia, Lebanon, Lesotho, Liberia, Liechtenstein, Lithuania, Luxembourg, Macedonia, Madagascar, Malawi, Malaysia, Maldives, Mali, Malta, Marshall Islands, Mauritania, Mauritius, Mexico, Micronesia, Moldova, Monaco, Montenegro, Morocco, Mozambique, Nauru, Netherlands, New Zealand, Nicaragua, Norway, Oman, Palau, Panama, Papua New Guinea, Paraguay, Peru, Philippines, Poland, Portugal, Qatar, Romania, Russia, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, Samoa, San Marino, Serbia, Seychelles, Singapore, Slovakia, Slovenia, Solomon Islands, Somalia, South Africa, Spain, Suriname, Swaziland, Sweden, Tajikistan, Tanzania, Thailand, Timor-Leste, Togo, Tonga, Trinidad and Tobago, Tunisia, Turkey, Tuvalu, Uganda, Ukraine, United Arab Emirates, United Kingdom, Uruguay, Vanuatu, Venezuela, Vietnam, Zambia, Zimbabwe, Taiwan.
YMMV. Confirm before travel (especially given that many EU rules will change sometime in 2015).