I love living in Warrington, but I can see that moving from London will be a huge cultural shock.
We do have an Asian community which is mainly centred around the town centre and near the hospital - neither areas I would recommend given your requirements. They tend to be old families and descendants who have lived here for decades.
Areas to avoid Whitecross, Dallam, some parts of Latchford. Hood Manor and Old Hall aren't fab but aren't totally awful either.
I live in Orford which is like saying "hi, I'm a benefit scrounging scum bucket" to some, but actually it's lovely where I am and the public transport is really good (but expensive) and I can drive 10 minutes into the busy town centre or 10 minutes the other way and be in lovely countryside. Around Orford Green you get nice 1930's 3 bed semis for around £140k. It is busy traffic though.
Great Sankey is lovely (I grew up there) but agree the traffic is horrendous and avoid Chapelford at all costs. I just don't understand why that place is so bad, its new build and should be lovely but there are so many problems there.
Good high schools :
Great Sankey
Penketh - previous bad rep but believe its a good school now
St Gregory's (Catholic, Sankey)
Cardinal Newman (Catholic, Latchford)
Beamont Academy (Orford) - previous bad rep but has turned around and had a lot of money pumped into it
Lymm - best in the area (note: Never say that Lymm is in Warrington, big faux pas to Lymm residents 😂)
Bridgewater (Appleton)
Kings Leadership Academy (Woolston) my boss' girl goes here and they rage about it, relatively new school.
High schools to avoid -
Padgate Academy (Padgate) .
Sir Thomas Boteler (Latchford)
Lots of redevelopment going on in the town centre, great shopping centres dotted around and I find there's lots to do (more takeaways than we need though!)
I like being in the middle of Liverpool and Manchester, all the benefits of the cities without being too close. Train to Manchester Picadilly takes 25 minutes.
I did see your other thread and wanted to suggest Warrington but I wasn't brave enough with others suggesting Didsbury and Wilmslow etc 😂