There are two airports in Osaka. Kansai (KIX) handles both domestic and international flights and has a rapid train link to Kyoto (73 minutes). Unfortunately ANA doesn't fly any of its longhaul routes out of Kansai (nor is there a connection to NRT). KIX has NH codeshare flights to Bangkok and Singapore from KIX but only offers services on its own metal to China and Korea. Air Canada flies to Vancouver twice a day out of KIX and United has daily flights to San Francisco and Chicago. All these flights can be booked with NH numbers.

Itami is physically closer to Kyoto. You need 90 minutes to change planes at Narita and there are only 2 flights a day, one operated by IBEX. There is a bus service to Kyoto station that takes 55 minutes.