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Do you have a car? If so, you could head across to Coromandel Peninsula. Great beaches, scenery. Or head north to the Bay of islands. If looking for something more spectacular/cultural Rotorua for the thermal wonders and Maori Culture. You could combine Coromandel with Rotorua with a car in a 5 day round trip. Bay of island is harder as it is a one way trip up and back the same roads. Still lovely though.3
Not quite one way up if you take the Kauri Coast road one way and head on up the west coast then cut across to east coast once you get as far as the Hokianga Harbour then come back down SH1.
