The main city on the Taranaki peninsula, in my opinion, New Plymouth is among the nicest cities in New Zealand. Located at the edge of Egmont National Park, where Mount Taranaki is in the center, New Plymouth has an ideal geographic location between the sea and the mountains, diversified in activities offered.
Having stayed in this city for two months, I suggest you visit the local museum in the tourist information center. This museum traces the arrival of the first Maori tribes in the area, then that of the colonists. One annex introduces how the country's way of life has developed, while another focuses on the geologic formation of the peninsula. In short, it's information which allows for a better understanding of the changes of Taranaki and New Plymouth, in a nutshell.
If you are traveling through New Zealand between December and January, enjoy a nice summer evening by going to the festival of lights in Pukekura Park. Many national artists and bands perform for free on one of the three stages set up for this event. During my stay, I was able to discover a New Zealand reggae band that I highly recommend: Ddub.
Finally, a two day trek allowed me to reach Taranaki volcano. The view from the top is definitely worth the physical effort... However, it is important to be in good shape so that the climb doesn't become a nightmare!