Tokushima
Tokushima is easily accessible by bus from Osaka. The trip is about 2 hours from OCAT and round trip costs about 7000 yen.
Tokushima City is a lovely city with many canals running through the city center that have charming boardwalks built around it. There are also lots of shops around the station and some attractions further away such as : Tokushima is probably most famous for its Awa Odori Festival in August where thousands take to the streets to dance and about a million people come to watch. If you are planning on going to check it out, book early as hotels and buses etc will fill up!
Awa Odori Kaikan
About a 15 minute walk from Tokushima station, this is a museum dedicated to the Awa Odori where you can see the costumes and musical instruments used, see a show and try it out yourself. A bit touristy but if you have a special interest in traditional Obon dance it's worth a visit. On the first floor of the building there is a large gift shop selling all things related to Tokushima so if you have omiyage to buy, it's a definitely worth a stop.
Mt. Bizan - Eyebrow Mountain - Ropeway
On the fifth floor of the Awa Odori Kaikan is access to the Mt. Bizan ropeway the highest mountain in the region. The ropeway is 600 yen one way but you can also get set tickets that combine it with the Awa Odori Kaikan. One a clear day you can see Wakayama and Okayama prefectures from the top and even when the weather is less cooperative you can see some nice views. If you prefer to stretch your legs there are a number of easy trails up and down the mountain that pass by various shrines as well.
Naruto Whirpool Park
The wildest water in Japan! Between Awaji Island and Tokushima Prefecture is a narrow straight that has very dramatic tide changes. Also in the area are various observation areas and a museum explaining the tides indepth and how the bridge was made, it seems more geared towards children though. It's worth it to do some research and time your visit with a full or new moon and when there is a peak low tide. The April and March full moons are said to be the best time to visit. If this is all you want to see in Tokushima, the Naruto Koen is its own stop on the high way bus tours so you can get let off, take a tour and get back on a bus all in one day.
There are two options if you want check out the whirpools. One is the Uzu Michi - a special pathway under the Onaruto Bridge with special windows in the floor where you can have a bird's eye view of the water. Admission is 500 yen. Second is going on a cruise boat and getting up close and personal - hang on to your camera! Cruises are mostly under 45 minutes and are around 2000 yen totally worth it.
For more information on the whirpools including tide times and cruise information check out here http://www.uzusio.com/uzu.html