With such little time in Kyoto I would urge you to book a tour guide - preferably one with a car as (just as robyng has implied) the many highlights and attractions are widely dispersed around a far from scenic city.

I have given the recommendation by robyng to three work aquaintances who found themselves in a similar position to you (they had just one day to see Kyoto before returning from a conference in Yokohama). I have heard very good reports from both groups.

The thread is here: http://flyertalk.com/forum/showthread.php?t=551191 - the guy is very popular, so if you want to do this, book as soon as you can.

Whether you stay in Shinjuku (Park Hyatt) or near Tokyo station (FS) may depend on how early your flight back leaves Narita on your day of departure.

I understand that there are trains that run straight to NRT from Shinjuku, but they are few and far between. It will be easier to get to NRT from Tokyo station.

If you let us know the time of your departing flight, we can give you a better answer.

(Again - you can get the bulk of your luggage sent directly to NRT with the Takkyubin service either at KIX or at the Westin. Were you able to get one of the Japanese style rooms there? - I been led to believe that the variation of quality between different room types in this hotel is considerable)