Akita is a city made for walking, especially for going to Kubota Castle, Kanto Matsuri Festival and the Akita Citizens Market. For places further away, a bus is the best way to get around, particularly during the day where services are reasonably frequent. In a larger group a taxi may also be a good option. The city does not operate trams or subways, and while there are Japan Rail (JR) services, the other railway stations are quite far from most attractions in the metropolitan area, except perhaps Port Tower Selion.
The main bus terminal is at the West Exit of Akita Station. While some buses go from the west to east exits, it is actually easier to get off at the West exit and walk across, for example, if you want to go to the Toyoko Inn.
While buses on the main arterial roads are quite frequent (about once every 5 minutes), the frequency drops to half hourly for some point to point services, like the one from Akita Railway Station to the Observatory deck at Port Tower Selion. My tip is that you note the departure times when you arrive at Port Tower and time your visit to the observatory accordingly, which in my opinion, half an hour is more than adequate, unless you want to stay for a substantial meal. If you do miss the next bus, the alternative if you are adventurous and have a good sense of direction, is to walk east through the warehouse district to the nearest main road where the buses run every 10 minutes back to the city. The other alternative is to walk 15 minutes to the Tsuchizaki train station where there is a train every 20 minutes. The train is a lot faster though, taking 7 minutes to get to JR Akita.
Akita City buses also offer an unlimited rides day pass, which is sold at a manned ticket kiosk at the city bus terminal at the west exit of the JR Akita Railway station. The day pass, which costs around 1,000 yen, is really only worth it if you are taking longer trips on the bus, such as to Port Tower and the Youthpal Youth Hostel. If you don't use a day pass, a single ticket from JR Akita to Port Tower Selion is 420 yen for adults, and 210 yen for children.
There is also a Tourism Information Center near the ticket gates at the JR Station, on the walkway linking the east and west exits. If you see Yuki and Yumi from the Tourism Information Office, please say hi to them. They are very helpful and speak good English.
Please note the City Bus or the Day pass ticket does not cover buses to and from the Airport.