When conditions are right, usually in the winter, you can see Ruapehu, to the north along the beach. It's actually about 160 Km away, sometimes covered in snow.
It's also quite common to see the top of the South Island, over to the right of and a small distance from Kapiti, though sometimes you can also see a chunk of it right next to Kapiti on the right.
If you know where to look — straight out to sea, but angled to the north, then sometimes you can spot Taranaki. That’s more rare and you have to know where it is before you can see it usually. Taranaki’s some 178 Km away.
Photos are even harder to get, but it seems I managed one, with snow on 04 September 2017.
Occasionally you can look to the left of Kapiti and spot Tapuae-O-Uenuku, in the Kaikouras, at 192 Km away.
Then there are those extremely rare days where you can see all 3 maunga.
I recommend always taking a small pair of binoculars with you to the beach — you never know when they’ll be useful.