By train
There are no suburban trains. The Taeri Gorge Railway (http://taieri.co.nz) tel +64-3-477-4449 is a scenic tourist trip, ending at a small village called Middlemarch. Take your camera and lots of memory. The same company runs trips on the old Christchurch line as far as Palmerston, about 2 hours away. These go about twice a week in the summer.
By bike
There is a recycling centre down by the north-east end of the docks in Wickliffe Street which generally has one or two reasonable-condition bicycles lying about for $10 apiece. Carefully add air there's a service station due west back over the bridge and oil and you're set to go. You will also need a skid-lid/stack-hat/helmet, which are generally unavailable second-hand for liability reasons, but can be had new for $20 from the KMart in Meridian, between George Street and Filleul Street. There is another recycling shop called "The Recover Store" at the Dunedin Landfill on Brighton Road, Green Island.
Dunedin's hills are extremely steep but the town centre is reasonably flat There is an excellent flat ride out along the western shore of the Otago Peninsula to Harington Point, although it's a narrow road shared by lots of tour buses. A cycle track runs along of the industrial eastern shore of the harbour, about half way to Port Chalmers busy highway the rest of the way.
If you like a bit of a hill-climb, ride out along North Road to the Organ Pipes, a collection of rapidly-cooled rocks which have self-formed into organ-pipe-like structures. The walk along a bush track up to the Pipes themselves is very scenic and well attended by small, harmless wildlife. The ride up along the ridge of the Peninsula to Lanarch Castle is also good high-energy exercise.
If you like pushing a bike up a hill because it's too steep, dive off North Road onto Norwood Street, or cross to the east side of the Peninsula, or head straight up the hill behind The Octagon past the Beverly-Begg Observatory to suburbs with a view like Roslyn.
By bus
The Dunedin Bus Service is fairly average but cheap and does get you around. The main line service, St Clair-Normanby, runs every 15 minutes and is handy to about a dozen of the City's attractions. Most other routes are every 30-40 minutes. Some of the buses are not too attractive looking, but they are being added to by cast-off wheelchair friendly buses from other cities. The blue/gold coloured buses operated by Citibus (http://www.transportplace...) and the beige/dark red buses operated by Passenger Transport share all the town routes. Most drivers from either company will tell you where to find the right bus if you ask nicely, or you can ask the Otago Regional Council (http://orc.govt.nz) or call 0800-474-082 free from a cell phone, but only during office hours.The Peninsula bus route from the Museum is a good way to see the Peninsula, unless you're terrified by oncoming traffic: in places the full sized buses are wider than the lanes they travel in. The traffic is generally used to this and travels very cautiously. All Buses on the Peninsula service are Wheelchair Friendly.