I would not do Te Anau as it is (relatively speaking here) remote. I would suggest Wanaka instead. Kaiteriteri is great, but you could also look at Mapua as an alternative to be closer to town. I was in that area in April and had lunch in Mapua and used Kaiteriteri as my base for Abel Tasman. I agree with Lake Taupo, it is a great area.
I like it as a whole and think it is a great plan. The only part you are missing would require a 4th stay, but could be an alternative, and that is Bay of Islands. It would be hard to eliminate one of the 3 to swap for BoI though.