It would be most helpful if you can provide more info before we can try and help.
Info like which city/town are you based in, what class do you wish to travel in.
Air New Zealand FF program leaves a lot to be desired IMO because of:
- points are tied to a $ value
- limited award space on their aircraft
I would say Velocity, Krisflyer and Asia Miles is what I would focus on if I have Altitude points.
SYD-LAX in business 1 way costs:
95500 Velocity (flying Virgin Aust) or 104k Velocity (flying Singapore Air).
110000 Krisflyer (flying Singapore Air)
70000 Asia Miles (flying Qantas or American Airlines) 120k return
If you want a free stopover somewhere, that is a whole different topic. It adds a layer of complexity to it. Velocity in general doesn’t allow stopover for free. Krisflyer allows a stopover for U$150 from memory or 1 free stopover if booking return. I’m not terribly familiar with Asia Miles rules.