Recently Rich and I visited the Wellington City and Sea for the first time in a very long time. Its one of my favourite museums in Wellington. It not as overwhelming as Te Papa (I do love Te Papa but it's just SO big) and the displays are really interesting and well written.
My favourite part of the permanent collection is the "Wellington in the 20th Century" exhibition. Which includes and interesting fact for each year and some photos, sounds or other media.
There is also an exhibition on at the moment called Back & Beyond & Here - this is an exhibition which is mainly orientated at children and young people so its pretty fun. It has art works but also all kinds of interactive things like a tracing table and etch-a-sketch.