Easily identified by the "〒"symbol out front, post offices in Japan are ubiquitous. The Kyoto Central Post Office is located in front of Kyoto Station and is open for business 24 hours a day. The airmail rate for postcards is 70 yen to any overseas destination, an aerogramme costs 90 yen. Letters weighing less than 25g cost 90 yen to countries within Asia, 110 yen to North America, Europe or Oceania, and 130 yen to Africa and South America. All post offices provide a reliable international Express Mail Service (EMS), which is as good as or better than private express shipping services.
There are several options for international shipping, with the easiest by far being post offices operated by Japan Post. Their EMS (Express Mail Service) is speedy and reasonable. You can find more information at: http://www.post.japanpost.jp/int/ems/index_en.html
The post office also offers surface mail, airmail, and other services at affordable rates. FedEx also offers services in Kyoto. You can arrange pick-up or visit their downtown Kyoto office: http://www.fedex.co.jp/jp_english/dropoff/#fedex_ship_centersKyoto
Best of all, you can use your credit card or FedEx account number to make payments.