Chesterton is fantastic, near to town, nice schools, near the river. There are two sides to Chesterton - West and East, West Chesterton is perceived to be naicer, the de Freville estate is one of the loveliest parts of the centre with a price tag to match! But that may not be an issue for you if you're moving form London. East Chesterton is much cheaper but has a good community feel, lots of activities for young families plus you can park a car within a 2 minute walk of your house. Also within cycling distance of station and walking distance of the science park. Plus Chesterton is getting it's own station in 3 years time.
As Wilderrose says, there is a snobbery against Arbury which is historic and unfair. IME, Arbury has quite a lot of academics, drs, nurses, teachers etc living there because it's cheaper than other areas of the city, so the demographic is different to how it was several years ago. There is a little parade of shops in Arbury, called Arbury Court, with a good butcher and a small Budgens. The notice board in Budgens always has lots of community stuff posted on it.
Don't really know Cherry Hinton so can't advise there I'm afraid. It feels less central and more "suburban" that Chesterton and Arbury, but that might be my mis-perception. If you're renting you'll have a chance to get a feel for the area anyway, before you make a decision about where you will finally be living.
Cambridge is a great city, small enough to feel "knowable" , big enough to have lots of cultural stuff going on, and within an hour of London.