Waitomo is a little bit out of your way. Otherwise it depends on whether you like mountains or caves. Weather might be a bit on the spring side for Tongariro, but it would be my call. Game-day decision, I'd say.
Going there myself, will be take in Rotorua and Lake Taupo, and also Tauranga and Mount Maunganui on the Bay of Plenty for a bit of sun and sea on St Stephens Day.
I did black water rafting in waitomo and it was great but not sure what else there is to do in the area.
Re the op, rotarua is a pure 'must'. It smells but the Maori culture tours and the volcanic activity makes more than justifies it.
Worked or at least turned up in over thirty countries, never made it to New Zealand, a country I always wanted to visit. Bugger!. Scotland/Ireland with some sunshine someone once told me.
