To maximise miles on UA awards, I would recommend doing the stopover in NZ/Australia while making the final destination of the award in SE Asia. It is possible to go, for example, ORD-NRT-BKK-AKL-SYD-LAX-ORD (or something similar), which would be 80k miles in economy on a roundtrip UA ticket and a stopover in BKK, with the final destination as AKL. However, if you do something like ORD-SYD-AKL-BKK-ICN-ORD, for instance, with the final destination as BKK and a stopover in AKL, it would only cost 65k miles roundtrip. If using US miles, do the final destination as AKL and the stopover at BKK, because the mileage requirements are less for AKL than BKK.

BKK would be fine for UA/US award stopovers. SGN and HAN are nice places for shopping - especially for knockoff clothes! They're of good quality, I can vouch for that. Though it would be easier to do a stopover at SGN on UA miles than US miles because SGN is a UA destination but not a US destination.

How many miles do you have on each programme? PM me - I could help you look at a possible itinerary, if you so wish. If you have miles to fly F - you might as well route through FRA on LH F to hit the First Class Terminal too!