Ok lollystix where you live is going to depend quite a lot on what amount of rent/mortgage you can pay.
My first thought is somewhere in the inner suburbs, which surround the city centre. Ponsonby/Grey Lynn/Mt Eden/Parnell/Herne Bay/St Mary Bay/Freemans Bay all surround the CBD and afaik all have good primaries. They are all very nice areas with cafes, interesting shops etc.
A lot of people move to be in the high school zone for Auckland Grammar, it's a state school that has some of the best results and one of the best reputations of any school, private or state. Mt Eden (which is in the zone) is v nice, I rented there for years. Prices are high though, reflecting the popularity of the school (and the area as a whole) The Grammar website will have the zone map on. Another very good high school is Macleans which is further out to the east, bigger commute to the CBD though. If Sibble is around she may have more advice on schools as her dcs are school age.
Ponsonby/Grey Lynn to the west of the CBD are a bit more arty/left-field kind of areas in the people who live there, Parnell and Remuera to the east are a bit more moneyed/traditional (that's my impression anyway). A bit further out from Ponsonby are Western Springs/Westmere/Point Chevalier which are slightly cheaper, still less than 10 mins drive from CBD (maybe more in rush hour tho) and are good areas too. Pt Chev is the only one to have a nice sandy beach!
To the east along the coast from the CBD are Kohimarama/St Heliers/Mission Bay, all v nice, I think primaries are fine. I think the high school out there wasn't great but is much better now (Selwyn?)
North Shore also has a rep for mainly v good schools (primary and secondary, well there's intermediate too from 11-13 but I won't go on about that now) but the commute can be a pain.
These are probably the "nicest" suburbs but Auckland is so big and spread out there are loads of others that are perfectly nice, Mt Albert, Sandringham, Balmoral, St Johns, Meadowbank...I could go on but a lot depends on your budget. And how long you are prepared to commute. And whether you want to rent or buy. And probably other factors too!