Werrington is generally a nice area, and the older part (Werrington Village) is thought to be the nicest part to live in.
It's popular with families because of the various open spaces and play areas. Cuckoo's Hollow is also generally a nice place to go for walks. It's set up as a kind of nature reserve. (You can google it to see what it looks like).
You would also be fairly close to Werrington centre, which has a few shops (including Tesco, I think), a sports centre and a small library.
Peterborough's road system (the parkway) means that if you have a car it's fairly easy to get from one area to another, so you wouldn't necessarily be stuck with whatever is in Werrington. If you need to rely on public transport, the bus service is expensive and not all that great. (£4+ for a day ticket for an adult, and the child prices are almost as expensive as the adult tickets.)
I only know the schools by reputation. William Law is generally thought to be a good school. It's a C of E school though, and some people are put off by the emphasis on the religious side of things. It's a big school (400+ children) which means that the resources and opportunities tend to be good, but that can be offset by having to share them with so many other children. It really depends on what you're looking for.
Werrington primary tends to be the school that people choose if they prefer something a bit quieter than William Law. I don't know about the other schools.
The main secondary school is Ken Stimpson, which seems to have a good reputation as well as the use of the facilities at Werrington sports centre.
The nearest estates that I can think of are 'new' Werrington (tends to be fairly nice), Walton (not a great reputation and home of the much-disliked Voyager secondary school), and Gunthorpe (not too bad). None of them are in the same league as the notoriously horrible areas.
Peterborough city centre is not particularly nice. Many of the better shops have either left completely or have moved to one of the nicer shopping parks that are dotted around the city. The shopping parks tend to be much nicer and generally have free parking too.