I usually book a nice business hotel and do my laundry in the coin machines every 2 or 3 days.
As mentioned above, there is little for a first time visitor in Kobe or Nagoya. On the other hand, there is a LOT to see in and around Kyoto/Nara/Osaka during cherry blossom season. I'd re-do the itinerary.
The Japan Rail Pass is a very good deal if you have enough travel planned to make it pay. I almost always get one unless staying primarily in one area. The Rail Pass does place restrictions on what shinkansen trains may be used. The most frequent Nozomi and Mizuno trains are not available. That is not normally a problem as the Hikari trains are fast and comfortable. Also note that the Rail Pass does not cover non-JR trains.
Early April is peak season for the areas you mention. Make hotel reservations early.