Hello @Heidii .
Seem as you are at Mt Maunganui (known by locals just as “the Mount”) for several days, yes it would be good to visit Coromandel although that means back tracking quite a bit if you drive from Auckland to the Mount. It would have been good to stop on Coromandel somewhere on way down to the Mount. If you are committed to accommodation already at the Mount, sure, go back to Coromandel as there are beautiful areas, especially on East Coast of the peninsula.
Good idea to visit Rotorua during this period too as it isn’t that far. If you have another day free, I suggest visiting Hobbiton at Matamata because it is a really good place to visit, especially if you enjoyed Lord of the Rings, and/or The Hobbit movies.
This route is what I suggest. Leaving the Mount, you could go through Rotorua to Taupo but because you would have already been that route already, I have suggested a different route which isn’t much difference time wise. In Taupo, you could visit the any of these attractions. Near the end of day, I suggest driving to southern end of the lake and stay here. Staying at southern end saves a lot of travel time the following day to head towards Wellington. You can cook own meals in accommodation and if it is nice day, use the bbq and sit right next to lake. Being at southern end of lake, you get the northern aspect and being March, it is good. It is much more peaceful than Taupo.
You can drive to Wellington direct from Taupo or stop off somewhere. In Wellington, staying somewhere downtown is good because it is best to get an early morning ferry crossing. Getting to ferry is very easy drive along the waterfront.
On South Island, my suggestion would be to drive down the west coast, possibly staying at Franz Josef or Fox Glacier. This is a very scenic route. Depending on your timing, stop somewhere else and do some exploring. I know this misses out Christchurch. If you are in to heritage, definitely go to Christchurch, but also Dunedin.
So much to do with not enough time.
I’ve lived in Auckland, Mount Maunganui (my daughter lives there), and Taupo. The sea will be nice when you are there so enjoy swimming and possibly some fishing. Visit the Mount Ocean Sports Club more nice meal. I managed this club for 4 years many years ago. The activities around Taupo are immense. It is the action capital of the North Island, and Queenstown being the action capital of the South Island. I was a paramedic in Taupo for 4 years and my wife and I will live there again when we eventually return to NZ.
Be safe on roads. I’m unsure where you are from, but in NZ, stick to the left of road.
If you have any questions, don’t hesitate to contact me.
As @PaulPavlinovich mentioned, Cornwall Park in Auckland is nice, and also the Auckland Domain, and North head in Devonport (another place I lived for many years). Ferry between Auckland city and Devonport is very quick and convenient. The Auckland museum is free to visit most places and it is interesting.