Long-term Wandsworth/Battersea dweller here. Have family in Sutton and Croydon.
The short answer is that if Chiswick's your vibe, Sutton won't be.
Nothing wrong with Sutton, it's a perfectly good place to live and the schools are terrific.
But it doesn't have that bars/foodie/cafe culture that you would get in Chiswick or Clapham. Not to the same extent, anyway.
Clapham would be a pain for getting to Heathrow I would have thought.
Is your DH driving or getting the train to work?
Mate of mine used to commute to Heathrow from Richmond. She drove, or I think there was a bus laid on for airport employees. (Not sure about that one, it was years ago.)
Hammersmith might be worth a look. It looks hideous from the perspective of the gyratory, but get away from that and there are lots of nice places to eat, shop and drink. Plus it's on the river. Something of an arse for you getting to the City though.
I'd look at places on the train line into Waterloo, 'cos then you can get the Waterloo & City to Bank. Get in early enough and it's really quick. (When you say City, do you mean around Liverpool Street, as in the old City, or Canary Wharf/Docklands?) So: Battersea, Wandsworth, Putney, Barnes, Mortlake, Chiswick, Richmond, Twickenham. All decent places, plenty of 'stuff' to do (and eat and drink!) and you'd also be on the right side of London for your DH to get to the airport.
None of these parts are cheap and some will definitely be a hit-and-hope stretch for 500k but you know that (Oxford isn't exactly affordable either is it)