Best city for stopover with baby on flight from Germany to New Zealand?

My partner and I plan to spend six months with our baby in New Zealand. She will be 6 months old at the begining of our trip. We'll fly from Germany and want to break up the journey somewhere about half way so we can all get some sleep and hopefully cope better with the jet lag. The stopover should be somewhere with a similar climate to ours (i.e. can be sunny / warm or cool, but should not be tropical / humid / superhot) and it should not be too much hassle to get from the airport to a place where we can relax for a few days. This could be in the city or near the city.
My partner and I are both well travelled and have backpacked and/or lived on all continents.

What are your thoughts on a stopover in
Seoul
Taipei
Tokyo
Hong Kong
San Francisco
Los Angeles
Buenos Aires
Santiago de Chile

Any other recommendations regardings places for a stopover, airlines, practical tipps ... is also very welcome!

Thanks a lot!

I haven't been to LA or San Fran, and I haven't been to any of those cities with a baby, this is just more a general comments about flying long haul with a baby. We flew Sydney to UK with an 8 month old. We had a stop over in Abu Dhabi, just 48 hours and it was mostly just an opportunity to sleep and catch-up a bit before jumping back on the plane for the second leg. Based on that experience, where we had a 7 hour time difference Sydney and Abu Dhabi, our daughter was waking around 2am and staying awake for a good couple of hours, and then by 2pm she was done for the day, we'd have to drag her out of bed after her afternoon 'nap' and it was near impossible to actually keep her awake long enough to feed her her dinner. We did do some sightseeing, but it was pretty much limited to the time between breakfast and lunch. I guess my point is that unless you allocate a good chunk of time to your stop over, you are going to be very limited with how much you can really expect to see of any city in a few days. I would also stick to a destination that is a direct flight from Germany and is another direct flight to NZ, extra plane changes is just added hassle with a baby. Once baby has overcome the jet lag, you will have a great time in NZ.

@ lvuaja
Thanks for sharing your experience!
How long did your baby need to overcome the jet lag (and how much was the time difference)?

you don't seem to give the time of year for the trip. So Hong Kong could be hot and steamy, or cold and damp. San Francisco could be warm and foggy, or cool and clear. LA doesn't have a real centre and is a long way from its airport.

Singapore? Hot and humid but plenty of aircon refuges, parks, gardens etc.

@neverwinter
You're right! We will fly to NZ mid / end of September and return in first week of April.

Sorry missed your question, total time change was 11 hours, and it took about a week from arriving in the UK for her to adjust (on top of the 48 hour stop over) and about 10 days to adjust when we got back to Sydney. Obviously each day it got easier, I've just given total time it took to get her back to going to bed easily, sleeping through the night and napping at 'normal' times.

Thanks, lvuaja!

just to check something you've almost certainly thought of - are you Germans? If so can you stay in NZ six months? (If you are British then it isn't a problem)

Thanks, neverwinter. Yes we have - and we can!

splendid - six months is still not enough for NZ but you'll be able to see a lot at a relaxed pace.

I think with your timings San Francisco will be good. Although I still love Singapore.

We will now have a stopover in Seoul, both ways. In the end, it was the best of all choices - especially since we could make a reservation for a baby bassinett with Korean Air right away (which wasn't possible with other airlines).