You're gonna need a car to get to any surf from Albany.
Orewa on the east coast will be just north of you (15-20mins) Taka's (Takapuna) just south of Albany as well, pretty small and inconsistent though. Be prepared to wait a few weeks between sets, unless we get some cyclone swell from the pacific islands, even then you won't be bragging to anyone about it.
West coast is all good - Piha, Karekare, Bethells, Murawai. All punchy breachbreaks with the power of the southern ocean and roaring forties backing them up. It's not often there isn't swell there, though it can get a bit out of control if you're not confident, or out of your comfort zone.
Albany is a good 45 minute drive from Murawai, 30 mins or so from Bethells. There aren't any "towns" out west, more community style places. Pretty small and mellow. You can buy milk, bread and ice blocks, but don't expect too much. Fortunately for you Albany is the new home to the southern hemispheres newest/biggest mall
So anything you're likely to need is a short walk from Massey Campus. From memory there are already a couple of surf shops there anyway.
I'm out near Bethells, forecast for 4ft+ through this week. Enough for thrills, Water is colder on the westside which suits me because I hate heat, you can still go out in boardies though. Wellington in Summer isn't that cold either.