We spent a day exploring the peninsula while staying in Christchurch. It is easily accessible by rental car and you do not need to take a tour to see the sights. Highway 75 goes up and over the peninsula into the remnant crater, where you visit the famous town of Akaroa. We did not particularly care for Akaroa, finding it very touristy--lots of restaurants and very few shops of anything one would consider local.
We spent quite a bit of time hiking, exploring a smaller peninsula within the bay along Onawe Flat Road, near Duvauchelle before arriving in Akaroa (check it out on Google Maps). Upon leaving Akaroa, we drove the scenic route which takes you along the rim where you can drop down into the small bays on the north side of the peninsula. We sat on the beach in Okains Bay and took this incredibly small road (don't tell the rental car company) up and over a point into Little Akaloa Bay. It's just you and a lot of sheep enjoying the amazing views. There are even more Bays waiting to be explored.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.