Yes, I agree that it is good to stay at Sakuragicho area: actually, hotels close to Minatomirai or Bashamichi Station of the Minatomirai Line are good. Minatomirai is good for shopping and sightseeing in Yokohama, and Yokohama Royal Park Hotel, Yokohama Grand Intercontinental Hotel, Yokohama Bay Hotel Tokyu are the 3 good hotels in Minatomirai area, but they are not expensive. The more inexpensive hotels are at Sakuragicho and Bashamichi station area. It is good to take the Minatomiral Line eastbound to Chaka-gai (Chinatown) to eat Chinese cuisine.
To go to Shin-Yokohama to take the Tokaido Shinkansen to Kyoto, you have to take Minatomirai Line westbound from Minatomirai or Bashamichi to Kikuna and transfer to JR Yokohama Line westbound for one station or Minatomirai Line to Yokohama and transfer to Subway Blue Line to Shin-Yokohama.
Alternatively, you should take either JR Yokohama Line or Subway Blue Line from Sakuragicho Station to Shin-Yokohama Station.