If you are in Napier on a Sunday then the Hawke's Bay Farmers Market is definitely worth a visit. If not, Napier is one of the biggest wine growing regions in New Zealand, so I would recommend a wine tour and perhaps lunch at a vineyard.
Gisborne also has some great wine grown locally, and I noted on a local trip up there some cool looking local breweries.
Wellington (my home town) - if you are here on a Sunday I would walk around the waterfront to the Waterfront Market, have a browse and grab some food to eat from the food trucks/stalls. Highly recommend porno donuts if you have a sweet-tooth. Then I would pop into Te Papa (right next door). From there, it really depends on what you like - there are lots of local breweries in Wellington, so potentially worth giving them a visit. Parrot Dog (in Lyall Bay), Double Vision (in Miramar), Garage Project (in Aro Valley) you will want to uber to. Double Vision could be combined with a visit to Weta Workshop and a coffee at The Larder.
Here's a guide to some more - https://www.stuff.co.nz/travel/destinations/nz/wellington/123420347/the-ultimate-guide-to-wellingtons-brewpubs
Coffee is also big in Wellington. Lots of local roasteries.
I also found this tour - https://www.zozotravel.co.nz/taste-buds-tour-petone which will take you slightly north of Wellington to Petone, which is a bit of a foodie hub too.