Headed to NZ in 2 weeks for a hiking trip but will have one afternoon and one morning to enjoy the city before flying out.

Anything we MUST do? Any great restaurant recommendations? I've already got the botanical garden on my radar. Any thoughts on the International Antarctic Center?

I was there last month. The Antarctic centre is cool, if you have interest in the subject, as I did (mild interest). The Haggland rides are fun. They load a group of you into the back of it and take you over a wild course to simulate Antarctic terrain. Pretty wild, probably wouldn't exist in America's litigious society. The city centre has the hop on/hop off trolley that is pretty cool to do a full circuit of the area, but it's not overly exciting. Just kind of a nice little city.

Our flight to AKL is at 2. From what I understand, it's right by the CHC airport. If we got there right at 9, would 3 hours be enough time?

Yeah, you have it right. 3 hours is plenty of time. Since it's so far outside of the city centre it is a good plan to combine it with the airport.