Hiya - we stayed in Wellington for a week while we had a think about whether Wellington was where we wanted to live. We stayed right in the centre of the city, so very close to everything - it was a really unusual apartment type building, built on stilts over a carpark!! But it was really well equipped - lovely large open plan kitchen/diner/lounge, and 2 bedrooms/bathrooms downstairs. Had washing machine/dryer too so ideal as you are travelling with kids. It was called What'sNew on Boulcott; What'sNew also do apartments in other parts of the city centre too. Price wise it compared very favourably with the cost of a week's stay in a motel.
Here's the link to where we stayed
Whats New: Whats New on Boulcott - apartment accommodation wellington nz, furnished serviced apartments wellington nz, long term rental accommodation wellington nz
Maggie xx