Derby has plenty of decent suburbs. Allestree, Chellaston, Oakwood, Littleover, Mickleover. It's a nice size "city" that has most of what you need and is easy to get around (by car anyway).
The surrounding villages are also pleasant, Smalley, Breadsall, Kilburn.
The pit towns are their own little strange bubbles where Brexit is 50 years away and joining the Single Market is a political hot potato
They were rather interesting places to teach in, especially when teenagers think 10 miles is near the edge of the planet (special dispensation granted for Skegness
)
The smaller country towns like Belper, Melbourne and Asbourne tend to be nice.
There's been a lot of growth along the south side, Chellaston, Hilton, Etwall which can put pressure on school places.
Nottingham is more cosmopolitan, but it's more sprawling and congestion is more of an issue.