You should have hit Supparo. Did it in January 3 ? years ago. Land in Supparo, take train from airport to downtown, hotel on railroad station. Second night in diesel multiple unit train with sleeper berths to eastern tip of island, have breakfast, ride morning day train back in 18" deep snow. ON TIME. Found official guide like national timetable in bookstore in Supparo. All in Japanese, but the first pages are maps with page number for the schedules. Numbers are numbers. Figure out the characters for the major points from the map and you are good to go. To Hokodate in afternoon. Next day do tour of museum area inside the Seikan Tunnel. Is at a control / maintenance center for the tunnel. Train stops and one door only opens. Tour guide spoke no English but there were bi-ligual signs on everything, and we did manage some worthwhile communication in spite of the language problem. The multiple train run from Supparo (Hokodate in our case) to Tokyo is no problem. Thanks to tourist office in most railroad stations we kept a rolling game plan and a place to spend the night worked out about one day ahead. You could spend a long time in Japan and see a lot of things without evey getting over a half-mile from a railroad station.
Supparo has a replica 19th century village on the edge of town. Most facinating. We went to and from by city bus.