Hi Tony and Kathryn,
I'm a Tauranga (well Mount Maunganui) local - and stumbled onto this forum randomly. So I thought I'd have a go at answering some of your questions. (My husband is from England and he moved over here 10 years ago.)
1. For starters Tauranga is obviously a lot smaller than Auckland and the pace of life is a lot slower. I'm not totally biased or anything but I would say it's an excellent place to live and bring up a family. I suppose you would have visited before since Auckland is not far away. One thing I would say is that in my opinion Tauranga can lack a little bit of spark - but life is what you make it I suppose and there are lots of good cafes, restaurants, watering holes etc.
2./3. As for best place to buy/schools - I'm probably not the best to recommend as we are just renting a place at the Mount at the moment. So these suggestions are based on what I know.
For family - areas such as Otumoetai, Brookfield, Matua, would be good places to buy as are close to good primary schools (Good schools in these areas Pillans Point School, Matua Primary, Otumoetai Primary) I know are good. These are the more central places.
A bit further out (but in Auckland terms not far) The suburbs of Welcome Bay and Pyes Pa offer good lifestyle options. x
Cheaper areas to buy - would be perhaps Greerton, Gate Pa. (Greenpark School is very good)
I'm a bit of a Mountie so I would probably look to buy at the Mount - but I believe it's more expensive and maybe you get less for your money.
I do know Papamoa seems to be a place for young families wanting to be near the beach and they a rebuilding the highway so it won't be so much of a pain getting out there.
4. There are loads of young families living here so you're wife would easily meet other mums - good groups like Active mums (I think their on facebook?)
All the best!!!