The Telegraph station is a must see in Alice Springs, and now is home to quite a few caches within a couple of KM. There are couple of trails that lead from town to the Telegraph station. Today, I took the Spencer hill track to the telegraph station and return along the Stuart track. In all, the walk was about 7.3 km, and I did it in 1 hour 10 minutes, and that was hiding these few caches along the way.
The Spencer hill track takes you close to the river, while the Stuart track leads through the rocky ridges. These trails are very well marked and well maintained. Try and do the same loop and check out the fantastic rocky landscape that surrounds the north side of town; which is very contrasting to the landscap south of the West Mac's.