The Cheshire plains are very flat. So immediately south or east of Cheshire is river floodplain, can be very claggy / clayey. There is Delamere and Llandegla for organised trails, and all the further afield places in a day trip (from Lee Quarry / Rivington / Peak District to the east/north-east and the Snowdonia centres to the west). For nice cross-country type riding consider the Clwydian Range https://www.ridenorthwales.co.uk/agents/the-clwyds/
The areas into the Cheshire Plains are very ‘nice’, typically middle class who commute (or one of the family commutes) to the big city jobs, or large estate / land owners. It is essentially ‘rural’ with very few places having a good bus service and most kids commute to their schools unless you live in a big village. For the type of work available in the immediate area, typically call centres, industrial plants (Airbus, Vauxhall, Tata, Stanlow/Runcorn), the rural bits south and east of Chester are expensive for the area. Having said that every area will have social housing provision and there are stark differences between different villages.
If you are looking immediately south on the River Dee do check for flood risk even if far from the river. And be aware traffic can be atrocious, no matter where you are commuting to/from, there are a lot of people commuting across the region and it makes rush hour awful. But if you can work from home it’s lovely!