JR "Azusa" limited express trains require just over 2.5 hours for the journey between Tokyo's Shinjuku Station and Matsumoto. The one way trip costs 6620 yen and is covered by the Japan Rail Pass and JR East Nagano Niigata Area Pass. There are one or two trains per hour.
Take the Hokuriku Shinkansen from Tokyo to Nagano (80 minutes, multiple trains/hour) and transfer to a JR "Shinano" limited express to Matsumoto (50 minutes, one train/hour). With a good connection, the entire one way trip takes around 2.5 hours, costs around 10,000 yen and is covered by the Japan Rail Pass and JR East Nagano Niigata Area Pass.
By local trains, the one way journey between Tokyo (Shinjuku Station) and Matsumoto along the JR Chuo and Shinanoi Lines takes about five hours, typically requires about three transfers of trains and costs 4070 yen. With a Seishun 18 Kippu you could do the trip for as little as 2410 yen.
Highway buses operate hourly between Tokyo (Shinjuku Bus Terminal) and Matsumoto (Matsumoto Bus Terminal near Matsumoto Station). The one way trip takes just over three hours and costs 3900 yen. Discounts apply when tickets are purchased online. Online reservations can be made through Willer.
Above fees and schedules are subject to change. Be sure to check current yen exchange rates.
Central Matsumoto can be explored on foot. The castle is about a 15 minute walk from Matsumoto Station. Alternatively, bicycles can be rented for free from multiple locations across the city, including the M Wing Building near the station, the Matsumoto City Museum next to the castle and selected shops and hotels.
The Town Sneakers are four tourist oriented loop bus lines, which cost 200 yen per ride or 500 yen per day (the one day pass also includes a 10% discount on admission to Matsumoto Castle). Buses on each of the loop lines operate approximately every 30 minutes. Besides the "Town Sneaker" buses, there also exists a regular network of city buses.
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