The only hot springs suitable for bathing are at Ngawha which is close to Kaikohe. These are quite different from others in New Zealand, the water being much "thicker" with chemicals - mercury was once mined in the area. There are other springs in the same general area, including a significant spring at Lake Omaper.
There is another area of mineral springs around Kamo but these tend
to be just warm rather than hot.
On Great Barrier Island there are rustic springs that are very worth visiting. They are included here because the ferry service to the Barrier leaves from Auckland. The best springs are a goodly 2 hours walk from Whangapara. Accommodation (including a DOC hut) is available at Whangaparapara and transport can be arrange from there though there is still a half hour walk to the spring. There are other springs, including the Peach Tree, in the same general area that involve a longer walk.