Yes, we also had the overnight on the Millenium in Kobe and enjoyed 1.5 days in Kyoto. Stayed at the ANA Crowne Plaza Hotel adjacent to the Nijo Castle. Chose it since they have non-smoking rooms, was centrally located and was very close to a subway station.
The train system in Japan is excellent. We initially used it pre-cruise to get from Narita to Yokohama. You can purchase pre-paid Suica smart cards - to use for your train fares - near the train station at Narita. It is much more convenient to merely tap your cards at the train gate than to have to purchase individual tickets - and the fare card works for both inter-city trains and the transit systems in both Kobe and Kyoto. If necessary, you can add funds to the Suica card at any train station or even at some pharmacies/convenience stores
There is an automated transit system (Kobe Port Liner) to take you from the port terminal in Kobe to the train station in Kobe, where you transfer to a train from Kobe to Kyoto. You then have your choice of taxis, subways or busses to get you around in Kyoto. The rail trip from the Kobe port terminal to Kyoto Station is about 70 minutes and costs only about 1300 JPY pp one way (equivalent to about 13 USD.) And reservations are not required. Here is a great website to search for train service (schedules and fares):
Enter Port Terminal in the from box and Kyoto in the to box - along with your date and approximate time - then click on search. The Kobe Port Liner takes you from the Port Terminal to the Sanno Miya Port Liner Station where you transfer (short walk) to the adjacent Sanno Miya JR Station. The best connection from Kobe's Sanno Miya JR Station to Kyoto is a JR Special Rapid Service train without any change of trains and only about 5 intermediate stops (including the main train station in Osaka.)
Note: the bullet train between Kobe and Kyoto leaves from a different station in Kobe and it takes longer to get from the port to that station (requires an additional subway train ride) - thus the total time from the port to Kyoto is about the same or longer (depending on the bullet train schedule) but the fare is about three times as expensive.
We had no worries about our return since rail travel in Japan is very reliable and almost always on time (a 5 minute delay is considered a tragedy!) We left Kyoto around 5:00, got to the ship before 6:30 - in time for dinner - and the ship was not scheduled to depart until around 8:00. Just be prepared by knowing what train you intend to take out of Kyoto (time and departure track) and check out where that track is when you first arrive in Kyoto so that you don't get lost and miss the train. (If you tend to be concerned, then also get info on the next available train as a backup plan.)
Have a great cruise and a wonderful time in Kyoto!
PS I thought I had planned the loading of the Suico cards well so that we would use up all but a few yen at the completion of our trip - but I miscalculated and had to add a couple of yen to the cards before it would allow us to exit from the Port Terminal Station! Took us about 5 minutes to figure out how to do it - so don't play it as close as I did.