Peterborough is a very nice and clean city centre compared to alot of other places.
The only down side at the moment is that ALOT of immigrants were housed there in the last 2 years and the crime rate has gone through to roof!
Ive lived in and very local to there all my life and have always like it there.
If you have a decent amount of cash to spend then there are loads of good villages/towns within 25 miles.
Some of the nicest:

(Villages)
Warmington
Elton
(Towns)
Oundle
Stamford

There are also alot of nice areas on the outskirts of the city, Orton Waterville and Hampton are very nice.

Areas around the city to avoid:
Dogsthorpe, Paston, Welland estate