As for Westin Hotel, you can check-in at JR Kyoto station. You can take a hotel-provided shuttle bus to the Hotel. I remember it runs every half hour (at least). If you take a taxi, just tell the driver "Westin Hotel," then it will be no problem.
Also when you leave, you can pick up your luggage at the station. So you can look around the city and go directly to the station.

I do not think it is a bad idea to arrive at NRT and take Shinkansen to Kyoto.
It takes only 2 and a half hours.