How "nice" an area is to live in, depends entirely on how much money you have to spend on a property.
If you're moderately well-off then Walton or Ashgate are pleasant enough.
A step up from there would be Upper Brampton / Brookside / the poorer end of Somersall, if you don't mind the lack of any local amenities.
If you're fairly rich then the rest of Somersall and out into Holymoorside could be right for you.
If you're a millionaire then Old Brampton, and a few of the out-lying areas to the west are beautiful. But you are getting a bit far from the town out there and are going to keep your chauffer busy driving you to Morrisons every Friday.
As for the rest of the town, well trust me, you can tell a lot about a neighbourhood by how much the houses cost.
There are no property bargains or "secret enclaves" that no one else knows about.
Chesterfield is just like any other town, and if a house looks so cheap that anyone could afford it, it's probably because no one wants to live there.