The Yurrebilla trail is close to the CBD and at ~56km is good for 2-3 days.
If you're looking at doing a portion of the Heysen trail I'd recommend Cape Jervis to Encounter Bay with beautiful rugged coastal views. Or further North along the Heysen, there's great walking throughout Flinders Ranges NP.
Another option closer to Adelaide (also happens to be on Heysen) is starting at the Warren CP on Watts Gully Rd, about 8km North of Kersbrook. Really nice unspoilt bush for about 6km at which point you can head NE up Tower Rd. From this point there's any number of loops you can do through the forest.
Have a look at
http://www.heysentrail.asn.au/assets/go ... glemap.php to get an idea of your options.