Moving from London to Bristol — what areas should we look at?

Partner and I are both remote workers, finally cutting the London cord. Budget is around £400k for a 3-bed house with a garden. We've visited Bristol a few times and loved it but don't know the areas well enough.

We're early 30s, like good food/pubs, want to be cycling distance to the centre, and need decent broadband for work. Not planning kids anytime soon.

Which areas should we be looking at? Any areas to avoid?