I know some will shoot me down for this, but maybe consider looking at getting a credit card with points to help offset the flight cost. Two cards could probably get you US-Europe and Australia-US in economy and may even leave some miles for intra-continent flying as well.

I'm 22 myself and travel extensively and have been to about 2/3 of the cities on your list at quick glance. If you have any questions don't be afraid to PM me.

Back to the credit card theory... if you're a responsible individual (of which I assume you are) then strategically adding one or two cards may be beneficial if you plan on travelling in the future. You'd more than likely pick up a card that waives foreign transaction fees as well so that would be a decent savings, especially over the course of one month. So this is certainly something to look in to in my opinion as it gives you more cash flow to really enjoy the cities you're travelling to.

Of the cities on the list I'd probably leave out Bangkok and Honolulu, unless the miles/cost are minimal/work out.

This is just something quick I threw together...

Citi AA card (whichever is 50K bonus right now) will get you in Y US-Europe. Should leave you with enough miles for a single one way within Europe as well. Cover the European cities via train or LCC's such as EasyJet, etc. Qantas/Emirates runs pretty decent deals (under $1K in Economy) from Europe-Sydney via Dubai, so you could stopover there.
That will position you in Australia where you have access to other cheap carriers to get to NZ. The Chase United card would get you (if you can find saver availability) from Australia back to the US.