Off lead places - does it need to be fully fenced (I hate fully fenced).
There is the beach - all day in winter, and before 10am and after 8pm in Summer (when Daylight savings is in).
There are a couple of all year round all day off lead beaches in summer but I find you really don't want to be there between 10am and 8pm when it's hot anyway.
So in North Adelaide between Robe Terrace, LeFevere Terrace and Medindie road - are two ex cricket ovals, the one on the west/left is for small dogs and the one on the right (east) is for all other dogs - fully fenced.
There is another fully fenced one in woodville somewhere, and another on Oaklands road Marion, and another on Eliza Place Panorama.
Enfield Hockey field aka Somerset Reserve corner Kent ave and Murray street near Hampstead Road Clearview.
The not quite fully fenced places - most council owned sports ovals share with dog walkers when sport is not on.
Goodwood oval (between Fairfax and Chelmsford roads Millswood) is off lead when there is no sport on
Bailey Oval (near avenue road and south road Clarence Gardens)
Hazelwood park (near greenhill road and Glynburn rd) - excluding the playground
Hawthorn Oval - before 11am and after 4pm when there's no sport on. It's a bit of a mud pie at the moment.
I guess it depends where you want to live and what you can afford. There's some really nice big areas around Noarlunga and Happy Valley too. And quite a few bigger areas along Linear Park where you can let a dog off lead - when there's no organised sport. Check with council websites for where their dog off lead areas are.
Do you really have to move back to town. Some people commute from the hills - though, personally, I'd think that would suck.