From south to north New Zealand

Hello everybody. After a month in Australia, 15 follow in NZ..... I arrive in Christchurch on the 29th of Jan. In this city I rent a car for 3 days, to go around the mountains and lakes, staying in Lake Pukaki. Back in the city, where I stay for 2 nights, I head to Picton, on the mythical train trip "The Great Journeys of New Zealand" After 2 nights, I take the ferry to the capital, Wellington, where I stay for 2 more nights. The mountains next to the city of Turangi is the next destination. After 3 nights, I travel to the big city Auckland, where I stay until the 14th, to return home. Well, if any of these destinations coincide with yours, let's join? All the best Nelson