Id be tempted to hop over into derbyshire and the peak district, but it depends how far out you want to be and what you’re looking for. To the immediate north there’s a lot of ex mining villages/towns which can be a bit grim, although i exoect im out of date and they are all cultural hotspots these days. Out to the south and east it’s rural, but topologically uninteresting i think there’s a canal.
So i’d be looking to go over west and nort to Derbyshire, ashbourne, buxton, peak district, dove dale, edale, etc.
I grew up in Ashbourne and went to college in Nottingham, but not lived there for nearly 30 years so i may be full of it (and biased).