Thank you for all your replies!
I love Lack's suggestion - TYO - AKL - SYD - ICN - TYO with ANZ in C. I definitely want to try Air New Zealand and this sounds like a great opportunity to do so. I'll call local ANZ call center Monday morning.
If you wonder why I want to start in Asia/North America...
The thing is I want to try business class, but I don't have enough miles for flying to NZ in C from Prague. And I'd rather use reward flight's extra stops in NZ than in Asia. I am Ok with paying airfare from Europe to the US/Japan in Economy.