A. Transportation to Kyoto. Kyoto has no airport!
A1-1. It is convenient to take a Haruka limited express train bound for Kyoto. Trains depart every 30 minutes in morning and evening, with average journey time of approximately 75 minutes. They depart once every hour in 10:00--16:00. You can see the timetable here. The fare is 3,370 yen, including a seat reservation (subject to change). After arriving at Kyoto station, proceed along the platform in the direction of your train, and you will find Karasuma central exit on the left hand side.
A1-2. In daytime it may be more convenient to take an airport bus/coach from KIX to JR Kyoto Station. Timetable is here.
A2. From Tokyo--Narita (or Tokyo-Haneda) International Airport to JR Kyoto station by trains
By rail: Narita Express links Narita airport to Tokyo station, with average journey time of approximately 60 minutes. Haneda and Tokyo station is linked by trains. From Tokyo station, Shinkansen Nozomi and Hikari superexpress trains frequently depart to Kyoto. The average journey time is 2.5 and 3 hours, respectively. We recommend you to buy all train tickets at Narita airport in advance. The total fare for a one-way ticket will be 15,780 -- 16,490 yen (subject to change), including seat reservation. You can choose a non-smoking seat. Shinkansen platforms locate at the third floor of Kyoto station. After going down to the second floor, go out Shinkansen central exit and walk to the north along a corridor. Then you will find bus stops on the right hand side.
A3. From Tokyo--Narita (or Tokyo-Haneda) airport through Itami Airport to JR Kyoto Station
You may take a domestic flight from Narita to Itami Airport, which is a second airport in Osaka. An airport bus/coach takes you from Itami Airport to JR Kyoto Station in 50--60 minutes. The bus fare is 1,310 yen.
B. From JR Kyoto station to RIMS (map of Kyoto). There are three ways to get to RIMS from JR Kyoto station.
B1. By bus:
By bus: There is a bus terminal in front of Karasuma central exit. Take city bus No. 17 at bus stop A2, then get off at Kitashirakawa. The fare is 230 yen, and the average journey time is around 30 min.
B2. By taxi:
There is a taxi stand on the right hand side of Karasuma central exit. Please show this slip to the taxi driver. No tip is necessary. It costs 2,200--2,500 yen.
B3. By subway:
There is a subway Kyoto station (station no. K11) on the basement of JR Kyoto station. Take a subway bound for Kokusai Kaikan and get off at Imadegawa station (station no. K06). There is a bus stop on the left hand side of exit no. 3. Take a bus No.203 bound for Ginkakuji/Kinrinshako and get off at Kitashirakawa.