Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from West Virginia to Kyoto as you normally would.
This is defined as Charleston Yeager Airport (CRW) and Osaka Kansai Intl Airport (KIX). Codes like Osaka Kansai Intl Airport are often used to just call airports uniquely. Ready for more IATA code knowledge? These are related airports for your current travel destination: Nagoya Chubu Centrair Intl Airport (NGO), Osaka Itami Airport (ITM), Kobe Airport (UKB), Toyooka Tajima Airport (TJH).