Budget
Being NZ, if you want Fish and Chips, you go to a true fish and chip shop for them, and being a student town, you can expect to find some very cheap take-away food near the university campus.
The Good Oil down George Street the main street has premium ALLPRESS espresso coffee, fantastic edibles from the cabinet made fresh daily, and a full al a carte brunch menu available, also on Fridays from 6PM they host some of Dunedin's top acoustic musical talent with fantastic Central otago wines and locally brewed ales available.
One interesting local speciality is kumara chips (http://www.kumara.co.nz/n...), made with a local sweet-potato variant and typically priced at about double the cost of potato chips.
The kiwis are also good at making ice cream, and many places including little delis and general stores at places like MacAndrew Bay sell cones for fairly reasonable prices e.g. $2.50 for a giant ice-cream at the Rob Roy on the corner of George and Albany st.
Midrange
For the desperate, McDonalds is at 232 George Street, where an internet cafe is attached. For the even more desperate, you can try the Dunedin favourite, a cheese roll - a mixture of grated cheese, onion and soup on bread toasted.
George Street is has many restaurants, starting about two blocks north of The Octagon in the centre of Dunedin. There are also a few interesting places on Albany Street, which runs across the south of the University Of Otago.
The Friday bakery in Roslyn village is recommended. A cafe and wine shop called RHUBARB (http://www.menumania.co.n...) across the road.
If you're looking for brunch type foods on Saturday the farmers market at the Railway Station has delicious delicacies such as crepes including gluten free, the popular "bacon buttie", Whitebait fritters, and baking as well as fresh fruit and veges.