The Skyline Walkway runs in the hills more or less on the north western edge of Wellington between Makara Road in Karori to Johnsonville. There are several entry points, so you can choose how long you want to be there and which section you want to do. These photos were taken at the Karori end of the walkway.
If you are short of time, the top of Johnston Hill at 360 meters and with a 360 degree view would be a good target.
If you have plenty of time, allow 6 hours for the trail end to end, mostly going up and down the ridgeline. You can also bike the trail, although it would not be for beginners.