We are looking for a hotel/apt/B & B that will allow early check in after flying Atl-LAX-AKL-Queenstown.

We'd like to check in around 11 am.

Any suggestions (other than paying for the night before)?

B&B's and others in NZ tend to be accommodating, since they know that some people come early by plane. I would suggest that you email the places and ask them. I'm sure they will try to help. We checked in our B&B in CHC about 11AM, since the room was available then. They may suggest that you just hang around there, in the common room, or have someting to eat, until your room is ready.

It probably depends on what time of year you're going and if they're full up, but my experience has been the same as Jed's.

The good news is that Queenstown Bella Vista said we could have check in at 11:30 am. I hope they mean it.

The determining factor will be if the previous guests have departed, and the room cleaned. In my experience hotels/motels are happy to let you have the room if it is ready; check in time doesn't come into it.
In NZ the standard check out time is 10am, and check in is 2pm. THis gives them 4 hours to clean the rooms. not just your room, but all the rooms, Obviously some will be finished before others, and if your room is one of these, or if they can move you to an available room, I am sure they will do so.