Before covid you could find flights from $150 Nz dollars between nz and Australia main citys.

The best places for hobbits would be matamata where hobbiton is hiding and the weta workshop in wellington

Depends when you want to travel. In Australia, avoid the tropics in summer as it's wet season (far north Queensland, the Kimberley, Kakadu). The NSW south coast is lovely if you're after a coastal get away.

Flying between the 2 countries its usually cheapest to fly into/out from Sydney.

We went to both countries in November 2019. We flew to Auckland, and also went to Rotorua and Queenstown. We flew from Rotorua to Queenstown. From Queenstown, we flew to Melbourne, via Auckland, and also went to Cairns and Sydney. We took domestic flights within Australia, because we only had 9 nights there. We flew to Fiji for a few nights after. We went on a tour and all the internal flights were included in the price, so I don't know how much they were. November was a good time to go, it was warm enough in New Zealand and not crazy hot in Australia. We went to Hobbiton in New Zealand, it was one of my favourite things we did.

Impossible to say what flights will cost, Covid has changed everything. I live in NZ but I'm from Australia. Used to be able to fly myself, husband and two kids for less than $1k return. Last time I checked flights were $2,600 one way.

Australia is huge, and NZ is bigger than it looks. How long do you plan? What time of year? A rough idea of something that's already on your list to start from? Your question is a little too open at the moment..