My flight departs Auckland at 7:00 PM. Is there a good hotel in Auckland that would give me (without extra charges) an extended checkout to 2:00 PM or 3:00 PM on the day of departure?

The Crowne Plaza did that for us.
We were on the Club level, and I don't know if that made a difference.

Just ask nicely!

Denada:

Most hotels are accomidating for the extra few hours - for the Hilton in Auckland we had the reverse problem by getting there at 10am - they had a 3pm checkin & we were using Hilton points and we had no problems.

In all of my travels I've only ever had 1 problem & that was in a situation where the hotel was oversold, with a large group ariving early in the afternoon.

Z

Of course, most hotels will store your luggage for free until later in the day. Or were you planning to sleep in? Aren't you going to do far too much of that on the plane coming back to N.America?

Store your luggage and do wandering around and shopping until its time to catch a cab/bus/shuttle to the airport.