Relocating from London

[Lynch2018]

Looking for a bit of advice....
Myself and family currently live in North London in a 2 bed garden flat.
We have two young children (3, 0) and a teen in her 1st year at university, plus a dog.
We need to size up, to a 3 or 4 bed house. We are both teachers, so buying somewhere bigger in London is just not affordable.
We have been thinking of moving down south near the Bournemouth area, particularly Christchurch.
My younger brother lives in Southampton and my husband has some family dotted around Bournemouth.
The move won't be for another 2.5 years, but want to be well informed before we consider moving.
Not 100% sure about budget yet but likely £500,000ish (could be more).
I'm basically looking for advice on areas to investigate further. Needs to be family friendly and not quiet/remote as we're used to living in a big city.
Any help would be much appreciated.

Thanks,
Emma

I have family in that area although I don’t know Christchurch that well. Lymington is lovely but you’ll need a slightly higher budget, between 500-600k a lot of decent properties appear.

Youll find plenty in budget around New Milton, but I think they’ve had a fair bit of anti social behaviour there in the high street. Might be better now. Sway and Hordle are small but worth a look, very near to the forest, some nice character properties.

Milford on sea is small but quite buzzing (esp in the summer) at the same time, very nice but you’ll probably need deeper pockets. The occasional bargain does pop up though.

Thank you for your advice.
Will definitely add Lymington to our list.
The budget is hard to predict atm, all depends on how much we save in that time, how much our flat sells for etc.