Tokushima Castle
A brisk uphill walk from Chuo Park, behind the station, takes you to the castle ruins and a view over the city. The castle museum 9:30AM-5PM is set in an exquisite traditional Japanese garden — come early in the morning for a misty, meditative, and crowd-free experience.
Awa Odori Kaikan
An interesting museum devoted to the Awa Odori Festival. Exhibits include video and panoramas of the festival, and even a dancing Odobotto robot to show you how it's done! There are several daily performances of the Awa Odori dances ¥500.
Awa Jurobe Yashiki
Once the home of the samurai Jurobe, this is now a bunraku puppet theater museum. Performances are held at 11AM weekdays, with an additional show at 2PM weekends. Take a bus from JR Tokushima Station to the Jurobe Yashiki-mae stop.
House of Indigo
Located in an old house formerly owned by an indigo merchant. For a small fee ¥500-3000, you can dye your own piece of fabric with real indigo, and learn how to create one of the traditional patterns. Take a bus from JR Tokushima Station to the Higashi Nakatomi bus stop.
Tokushima Modern Art Museum
One of the most acclaimed modern art museums in western Japan, with work by contemporary Western and Japanese artists. Take a bus to Bunka-no-Mori Park from JR Tokushima Station, or walk west from JR Bunkanomori Station.
Tokushima Prefectural Art Museum
Natural and geological museum covering pre-historic Shikoku to the present day, with some hands-on exhibitions. Like the Modern Art Museum, it's in Bunka-no-Mori Park.