20 or 21 July 1969, depending on where in the world you were. Both the landing and the EVA occurred on 21 July in New Zealand. The times below are NZST.
My alarm went off at 6:50 am and I immediately turned on the radio to hear what was happening. Soon heard that the powered descent was due to start in a bit over an hour. Got to work at the Ministry of Works head office in Wellington at 8 am and the radio was already broadcasting what was happening at the moon.
Starting at 8:05:11 am there were 12 minutes and 29 seconds of hectic and tension-filled activity and lots of jargon that we couldn't understand when Armstrong and Aldrin fired up the Lunar Module's engine and began their powered descent to the moon's surface. There were a bunch of alarms which the folk in Houston figured were not a big deal, and they landed on the moon at 8:17:40 am. A few seconds later Armstrong reported, "Houston, Tranquilty Base here. The Eagle has landed."
Charlie Duke in Houston got a bit tongue-tied when he expressed the relief there: "Roger, Twan – Tranquilty, we copy you on the ground. You got a bunch of guys about to turn blue. We're breathing again. Thanks a lot."
I was too excited to work competently, so used up a half day of annual leave in the afternoon. Wandered around the shops in Lambton Quay and Willis Street and listened to bits and pieces on radios and TV sets. The TV broadcast was just radio plus talking heads in the NZBC studio. No live TV from the moon or overseas as we didn't yet have a satellite link for overseas broadcasts.
In the afternoon at 2:56:15 Armstrong first stepped onto the moon, and Adrin joined him at 3:15:16.
I wandered home around 5:30 and got a good view of the gibbous moon. It was pretty cool to think there were two men on it for the first time ever, and one man orbiting it.
There was no TV where I lived, so I didn't see the broadcast on the 7:30 news.
Manawatu Evening Standard, Tuesday 22 July 1969, page 6
Quick trip for Apollo film
NZPA Wellington, July 21
Some 4-1/2 hours after astronauts Neil Armstrong and Edwin Aldrin set foot on the moon today, New Zealanders saw a film of the historic event in a nation-wide television hook-up.
The 40-minute videotape was rushed to Wellington aboard an RNZAF Canberra bomber.
The videotape was recorded this afternoon at the Australian Broadcasting Commission's Gore Hill studios north of Sydney.
The Canberra carrying the tape left Kingsford Smith Airport, Sydney, at 4:15 p.m., and after a 2-3/4-hour flight, touched down at Wellington just before 7 p.m., an NZBC spokesman said tonight.
It was taken to Channel I in a car accompanied by a Ministry of Transport officer, in time to be shown in the NZBC's 7:30 p.m. news.
The spokesman said Customs and air traffic officials in both Sydney and Wellington gave the Canberra priority status, allowing it to clear formalities in the minimum time.
He said the corporation had not known until late this afternoon what time the tape would be available. The historic screening was rescheduled three times.
If the Canberra had been unable to land at Wellington it would have gone to Auckland, and the national network hook-up made from there.