Both Kobe and Yokohama fit the description that one of my friends gave for a certain U.S. city: "It's a nice place to live, but I wouldn't want to visit there." In other words, they have pleasant residential areas but little else to interest the first-time visitor.
The main attractions of Kobe are a Chinatown that consists of two blocks of restaurants and the old foreigners' section, which is a neighborhood of Victorian houses.
The Shinkansen actually runs through the hills north of the main part of the city, and at one point, you can see the long, narrow city and a section of the Inland Sea laid out below you.