Stopping in New Zealand before heading to South East Asia

The length of time you spend in NZ is entirely up to you. Decide what you want to see then plan accordingly. But you are right, NZ compared to SEA will eat a huge chunk of your budget. You also dont want to spend up large here then have nothing left for SEA. If I was you, I'd be a bit nervous as well. I've travelled in SEA for extended periods and you'd probably be looking at an average across the board spend of about US$50 a day.
May, June in NZ is winter.

and winter means short daylight hours.

If under 31, and want to give it a try, you could get the NZ WHV or the Aust W&HV.

The Aust one is Aud$460, a lot of money, but gives you the chance to get to legally work in Aust, as you already have enough to support yourself, its more so for you to feel how it is to work here.

Granted that your interest might not to be work in either, but just a thought.

Virgin Australia flies from the US, as does United/Delta etc, Qantas as well. Jetstar only flies from Hawaii though.

If you want to byapss Aust, but want to fly to NZ, then its Air NZ as the major carrier. Then Jetstar from there up to Singapore and then come down to Indonesia, or if you "dare", Garuda which you will transit Brisbane, Air NZ from the US to Auckland to Brisbane, and then from Brisbane Garuda to Indonesia.

If bringing cash notes, you have to declare it on the NZ incoming passenger card, in equiv of Nzd$10,000.

Edited by: spotty_dalmatian

If you (OP) don't want to go via Aust, you can go with Jetstar from Auckland to Singapore transit then to Indonesia, this bypasses you have to get an Australian Transit Visa, Air New Zealand will as I mentioned above, take you to Brisbane where you have to over night, out of the airport and in again, staying at one of the airport motels. Its an over night transit, off an Air New Zealand flight, and onto a Garuda one. I thought there was a day transit, but nope.

You could go to a travel agency, but cheaper to DIY, and learn from it.

You could go from Auckland to Singapore with Singapore Airlines, or Kuala Lumpur with Malaysia, both these countries don't ask for visas for US passport holders, no visa for stays under 90 days.

You could also go with Thai Airways from Auckland to Bangkok, then Air Asia from Bangkok to Kuala Lumpur, then down to Indonesia.

Edited by: spotty_dalmatian

OP, Jetstar fly to Singapore from Auckland and then on to Indonesia. It is NOT cheaper or easier to go to Australia to pick up an Air Asia flight. Or to fly with airlines like Air New Zealand, Singapore Airlines, etc.

US to China, then China Southern to Auckland, ???

OP didnt ask about airlines but is concerned with budget. On doing some working out, that $10,000 isnt enough for a month in NZ and the balance in SEA. A month in NZ would take at least $2800 of that. Then 5 months in SEA roughly $7500. As you say, OP. Enough for SEA. Have you thought of doing SEA then if money and time allows, doing a trip to NZ?

I would love any and all pieces of advice

Oh silly me. Flights and WHVs are your forte.