hi Uktokiwi,
I'd recommend Mt Eden, (it's the part of Auckland I think of as home so maybe I'm biased), it has a lot of the things you're looking for. Nice places to go for walks, really nice big Victorian-era houses (expensive but it sounds like that's not too much of a problem for you), good schools, lots of cafes and food shops, including really good bakeries, a big new supermarket, and close to St Lukes Mall (big & modern). Everywhere in Auckland is close to the sea but it's not too close. My parents' house has a view across the city to the Waitakere Ranges but of course the view would depend on where your house was situated.
Happy hunting!