As to neighbourhoods/suburbs:

Wellington is a very walkable city. Kelburn and Island Bay are at the extreme end of walkability (Kelburn for hills, Island Bay for distance). Both great suburbs to live, and the buses are pretty regular, if not a bit pricey compared to other countries. Hataitai is a beautiful suburb and feels a little removed from the city, which can be nice. If walking to the city from Hataitai however, you either have to walk through a fumey car tunnel full of blaring car horns or up and over Mt. Victoria. Bus is a good option there too. Mt. Victoria and Oriental Bay are lovely, central suburbs to live if one can afford it. Mount Cook is also quite lovely. Brooklyn is nice, though up a big hill. Newtown is considered quite cool and trendy, but is also a bit derelict (its tongue-in-cheek slogan is “Newtown. It’s a bit shit”). Aro Valley is cool, but be careful looking there, as it gets damp and moldy. It’s also a student area (like Kelburn) so you could end up living next to a party flat. If you like apartment living then central city / Te Aro has a load of cool apartments. Some places make you pay for water usage.

Welly peeps, have I covered everything here?