I grew up there and DPs live near Pantiles. First off we lived other end and I went to St James. Historically there's been a very broad north/south divide in terms of the 'not so naice'/'naice' sides of town. StJ is north, Claremont is south. In reality there are a blend of lovely houses and cheaper ones wherever you go in the town. Agents always say 'sought after Village area' - that's in the south, off high street and near Claremont. Prices there and in several roads thereabouts are high.
There are some lovely roads up around St James and TWGGS. TW is a bit like anywhere in London that's zone 1 to 3 in my opinion - some parts have snob value but really anywhere within those zones could drum up a potentially lovely house and community.
Anyone being weird with you because you are multi-cultural family would be a cunt IMO. My folks and their mates certainly wouldn't bat an eyelid. Having said that, it's still not massively diverse, but it's becoming more so.
The whole town is a shopping Mecca IMO. All parts have something to offer; again north more high street and south more boutique, but exceptions in both cases.
For hanging out Pantiles & off High Street is best for me (but biased). Saying that there are some great places along London Road, Mount Ephraim and Southborough. It's biased towards pubs and restaurants; not many clubs. There are some late night bars though.
At the beginning it can feel a bit cold in terms of community but if it does, it's not personal and in time you'll just morph somehow to feel a real part of things. There are great villages and pubs around.
High Brooms a good alternative station for northside but you may struggle for a seat more. There's a direct commuter service to Cannon Street c.40mins, that should work for your DH.
And I'm done... PM me if you want; not there now but go regularly to see my folks.