The Port Hills on the edge of Christchurch are home to a massive network of trials for hiking and mountain biking, as well as scenic road biking, and popular rock climbing crags. This adventure description is only an introduction to what the Port Hills have to offer.
Park on the west side of Summit Road near Dyers Pass Road to unload your bicycle or start on the Crater Rim Track. Alternatively you can hike up from the valley on the (west to east) Bowenvale, Huntsbury, Mt Vernon, Rapaki or Bridle Tracks, all of which are shared use bike/hike tracks.
Once you are on the crest of the Port Hills I suggest either Biking Summit Road (which is closed for a long portion making for great cycling conditions) or walking the Crater Rim Walkway, both of which follows the crest of the port hills from West to East. Views NW over Christchurch, the Canterbury Plains and reaching out to the Southern Alps are beautiful. Views SE look over Lyttleton, Governors Bay and Banks Peninsula reaching out to the Ocean.
There are many places along the way to stop and hike up to a viewpoint, such as Mt Vernon, Rapaki Rock, Witch Hill, The Tors and Castle Rock. However, beware of loose rock and steep cliffs.