Itami (ITM) is closer to Kyoto based on the experiences of myself and my fellow tour group members this past November. Until Kansai (KIX) opened it was the main airport in the region.
Most flights to the Osaka region do go to KIX now, but there are a few flights from Narita to ITM [the route I took]. If you are taking a limo the time difference is about 45 minutes, but I imagine the train connections reduce that considerably.
This is a unique airport. It is built on a reclaimed island. I read that it is one of most expensive airport in the world. Services are alright. There are buses and trains from the Airport to Kyoto and major cities.
The Kansai Airport Limousine Service will bring you to Kyoto or other parts of the Kansai. It is a bus service and cheaper than the train and it is right outside the arrival hall. About 90 minutes and 2,300 Yen (with reservation) to Kyoto. Buy return tickets (cheaper) if you intend to return from Kyoto.
Another option is the JR Limited Express "Haruka". About 70 minutes and 3,690 Yen (with reservation) to Kyoto. Reserved and non reserved seats are available. A reservation costs around 500 Yen.
I came from Tokyo Haneda airport with a ANA flight which landed in Osaka, the closer airport to Kyoto.
I did not know ANA but it revealed to be a good flight company very punctual and fast with lagguages.
From Osaka airport I took a bus called airport limousine that took me to Kyoto main railway station.
You can take the bus tickets just outside the airport and the price is about 10 euros.
Kyoto does not have an airport. The nearest international airport is Kansai (KIX), which is south of Osaka. The Haruka express (train) links Kansai International with Kyoto JR station. The journey takes about 80 minutes and cost JPY3490 in 2006. This was for a reserved seat. If you are coming from elsewhere in Japan, shinkansen (bullet trains) stop at Kyoto JR station on the way between Tokyo and Hakata (Fukuoka).
If you want to come from Europe, Australia or America the best way to get into Kyoto is to fly to Osaka Int'l Airport (Kansai). The Airport is located south of Osaka on a Island. Most International Airlines are flying into Kansai. JAL and ANA are operating also International Routes to many over sea destinations.
From Kansai Airport you get within 70-80 min. to Kyoto Main Station. After Immigration at Kansai you get into a big hall, take the elevator to the Railway level and there are counters to take a ticket for if you have pre ordered a Japan Railway Pass you can pick it uf here. Take the Haruka Express to Kyoto, it is leaving around every half hour and it stopes in Osaka, Shin-Osaka and from there it goes non-stop to Kyoto (on the picture a Shinkansen arriving at Kyoto Station).
The One-Way Ticket Kansai-Kyoto cost up to 45USD.
Enjoy your trip...
The nearest international gateway to Kyoto is through the Kansai International Airport which is in the city of Osaka. A high-tech airport unrivalled by any in Asia, this is one place you must take time to explore, just to amaze oneself with the ingenuity of the architects. Built on a man-made island, the airport is already sinking every year!