Christchurch is a walkable city, and many of the top attractions are within a short distance of each other. The tramway is a great option for getting around if you want to rest your feet, but it is not necessary for this itinerary. Taxis and rideshares are also available if you prefer, but they will add to your overall costs.
If you have more time, consider adding the Cardboard Cathedral, the International Antarctic Centre, or a trip to the Port Hills for panoramic views of the city. If you have less time, you may want to skip the Container Mall. Make sure to wear comfortable shoes and dress in layers, as the weather in Christchurch can change quickly.