Oxford. Oxford Oxford Oxford.
The only disadvantage is that housing (renting or buying) is ferociously, staggeringly expensive. But if you live there you can see why.
Looking at your list of requirements:
It’s the most (or one of the most, I forget) diverse cities outside London. (You can google the data.) Given that, I’d assume the state schools reflect that. And obviously some of the most sought after prep boarding schools are clustered in and around the area, so that also attracts an international pupil body.
Middle class professionals from different backgrounds? Well, people come from all over the world for study or research purposes, and stay for the burgeoning career opportunities in science and arts and social sciences, not just in Oxford but everywhere including London.
It really does have an astonishing amount of green space in the centre of the city. It’s easy to feel a little sorry for tourists who arrive for a couple of days, find themselves squished amongst a million others on the High St, or crocodiled through a couple of colleges, and then go home wondering exactly what they were there for. You need to live there to begin to appreciate the wealth of parks and meadows and woods and weirs - in addition to the college gardens you may have access to as a resident.
Commuting? 55 minutes to London by train. Or there’s the Oxford Tube (a bus) if you prefer.
Oh - the other disadvantage is that traffic in and around the city is beyond ghastly. Don’t plan a life that depends on driving through the centre at all. Walk, cycle, scoot, take the ample buses.
Look - I remember Oxford in the 80s when there might be only one Black face amongst half a dozen colleges. And they wouldn’t be from the UK. Things have changed so, so much.
(Maybe skip this bit if you’re not Black …)
The universities are falling over themselves to attract and shout about Black researchers. It’s still a bit - I dunno - if you can wear a Global South badge you’re celebrated, if you fought your way through gang violence on a council estate you’d better be working on a PhD about that (rather than cells or atoms or whatever). If you’re just an average middle class Black person who doesn’t identify as an outsider or disadvantaged - you’ll be considered very much less exciting.
But, the test - when you pass another Black person in the street, you don’t feel the need to nod to them - because neither of you is rare now.
I can’t recommend the place highly enough - despite all the rough and tumble of city life, and the competitiveness of so many clever people politely elbowing each other out of the way.