Day trips from Auckland, is Agrodome, Rotorua and the Gloworm caves worth a day each?

I'd say yes.
They are some of the top tourist attractions in the North Island and are different to what's in the South Island. I like day trips even with an early start as you know you are coming back to your hotel afterwards to collapse in bed!
The Agrodome is in Rotorua. Depends if you have been to other thermal areas like Yellowstone or Iceland as some people find Rotorua a little 'underwhelming'. But it has Maori culture there so it's worth going.
The Waitomo caves are in another direction and if you have not seen glow worms anywhere else it would be worth it. Great Sights offer a trip to both in a day and takes about 13 hours all up. https://www.greatsights.co.nz/new-ze...ckland-return/

If it's possible for you to rent a car and spent a night or two visiting these places, it would be worth your time. Lovely scenery and you don't have to rush, plus you could do blackwater rafting in Waitomo if you wanted.

Lee Ann