I used to live near Newark, albeit some years ago..and I now live in Peterborough of course.
I still visit relatives in Newark and do enjoy the town centre. It's got far far more character than p' boro. There are a lot of travellers there. There are a lot in p'boro as well..Immigrants....ditto.
As said, there are a lot of nice villages nearby, I used to frequent them all in my youth, but apart from visiting a local pub, which are generally relaxed, I can't see anything else to visit them for apart from the general nice surroundings.
It's all relative. Newark's not a jewel, neither is Peterborough, but a visit to the town centre is always nice, it at least has some smaller independant shops..not just the faceless stores we have here.
I don't mind Newark at all.
Cycling...sorry, no idea.