@chevin thanks so much for posting the follow-up. It's very informative, but also so nice to have a recent experience posted for knowing what to expect.
An update from me. Yesterday I had the medical exam at CityMed (9am) and dropped off the documents to the Consulate before (8am). I'll post a detailed recount -- never know which little piece of info someone might find useful (like I have - thanks everyone!)
Rescheduling medical:
I originally had it scheduled last week, but my flight to AKL was canceled. Rescheduling with CityMed for this week was no problem, but they mentioned the US immigration medical can be one of the trickier ones to schedule because they need nurse, doctor, and radiography appointments to be available all together. That said, I got the day I wanted.
Time required before interview -- they use digital forms. Everyone advised that it takes about 2-3 days for the test results to come back, and for them to be sent to the consulate. My (rescheduled) medical was 8 days before my interview; everyone seemed to think that would be more than enough time.
Accommodation, etc:
I stayed at the Rydges on Federal Street. Price was OK, ~170 NZD. I joined the 'PriorityGUEST' rewards club when I booked on the website. It was free to join, got me a few $ off the booking, and 20% of food/drink (although the meals at the hotel were a bit spendy so I didn't end up going there).
I caught the SkyDrive bus. $17 each way. Goes from the Auckland Airport domestic terminal to the Skytower (2 blocks from the Rydges). Can book ahead online (same price) or the driver has an EFTPOS machine and most people were just paying by Paywave as they got on the bus. Double-decker bus, lots of room for people & bags, very comfortable.
There is an NZ Post (for the oft-mentioned courier bag) on Wellesley St West. It doesn't look like it from the street (esp. with construction) but it's there. You go down an alleyway - if you're on Wellesley St West looking at the Wellesley Centre, it's on the left. Go down the alley and the shop is on the right. It's small, but has the bags.
Dropping off documents:
Arrived early, about 7:45am. The security guard was there but no-one else. As you turn left out of the elevator, there are 2 drop boxes against the far wall - one for immigration documents. I think this is probably where you drop the documents, but I wasn't sure (and didn't want to put the pack with all the original certificates etc. in the wrong place!) so I asked the security guard. He just ended up taking the packet, scanning it through the x-ray machine, and saying he'd sort it out. Easy drop-off.
Medical:
Got in ~20 mins early to fill in paperwork. The paperwork was just a general CityMed registration form, no extensive background questions at this point. Handed it back and they said to go to Waiting Room 1.
Appointment was scheduled 9am, got seen ~9:10am.
First stop was nurse #1:
Passport
Quick eye test (I normally wear glasses but asked to try without, we went to the second-from-bottom row and he called that a pass).
Took height, weight.
Took a urine sample. Bit awkward because you have to walk through the waiting room to get to/from the bathroom, but what are you gonna do. Trickiest part was washing hands while trying not to drop the tube.
I think this was where I got the test forms to take to each person (some wanted them, some didn't).
Nurse sent me to Dr. Donna:
Wanted to see record of vaccines - couldn't accept the print-out from MyHealth because it didn't have my name on it. I logged into MyHealth on my phone and showed her it matched up, that was fine. I had printed test results for Varicella that I got a few weeks ago because I had no proof of having had chickenpox. This did have my name on it and was fine. I also happened to have my Plunket book with vaccination records in it - she got reception to photocopy it and write my name on it. Apparently they have recently received an update about COVID vaccines. Her understanding was only 2 are required, but offered me the 3rd booster (was behind). I have a flu vaccine from July 2022 (so within the year) but they wanted a current one. Fortunately (at least in this case) I'm an asthmatic so these were both free.
Asked some medical history questions - mainly concerned with gonorrhea, syphilis, TB, and mental illness as far as I could tell. Asked about smoking, not much about family history. Controlled asthma was fine.
Physical test - stripped down to undies (a sheet was offered). Pretty brief, maybe 3 mins. Poked some organs, checked pulse, ears, eyes, tongue. No jumping jacks or anything like that.
Back to waiting room #1
Nurse #2:
Top-up jabs (current flu, and COVID booster)
Draw blood for blood tests
Then down to radiology for
Chest Xray - waited for maybe 5 mins, then about 1 minute having the Xray taken
All done.
Total time - arrived 8:40am (early), left 10:40am.
Hope that's helpful, happy to answer any questions!