Cricket is on a Wednesday evening, all year round, at the Canterbury cricket ground itself. Also in the summer on Saturday mornings in a village called Bridge. There are others, but these two are the well known ones.
Places... Well. Faversham has some very nice places, but if you have a good budget then Abbey Street is the place to go for (on the street itself, living round the creek at the end of the street is far less desirable). Advantage is that QE school is on the doorstep. If your budget is not that generous but still fair-middling then there are still some beautiful Victorian streets in the area. If you PM theoldestcat she can tell you more (am sure she won't mind my mentioning her).
Villages - Boughton has the convenience factor (7-11 shop, post office, local pub won the shepherd neame gastro pub of yr), also good bus route for when kids are older, and less than 10 mins drive to KC juniors. But it is less 'posh' than other villages. Hernhill is considered posher because more rural but it is also more isolated - getting a pint of milk can be a pain. Houses in Hernhill can take a while to sell because of the isolation.
Selling has a community feel about it and houses go quite quickly because of the ease to get to M2 and catchment for the primary school. Again not considered a 'destination' village to live in.
The 'desirable' villages, by the way, tend to be south and west to Canterbury not Faversham way. Bridge/wingham/littlebourne are the kind of places where people like Hugh grant, brad and ange, etc have at times been spotted (oh yes. And no school waiting list issues for them, apparently..).
Ospringe, well, no.
Oare hit and miss, personally I wouldn't. Shottenden has lovely houses but no bus routes/shops. Chilham lovely but a pain to commute to London from (high speed link ok but don't think there are many trains that stop at Chilham).
The road from Faversham to ashford has some really good value homes coming up quite often but the hamlets along it are a bit soulless and apart from a really fab riding school not much happening along that belt.
Blean is nice, as is rough common, but if you are coming for a lifestyle change you won't get the authentic 'country' feel (saying that, I grew up near there and the freedom of playing in those woods was great).
From Faversham toward sittingbourne there are some small villages which all seem beautiful, but the commute to anywhere is a pain, so I'm a bit biased against these.
If you are thinking of Kent college, then why not Whitstable as palace to live? Lots to do, characterful houses, quirky shops and very popular ( it's nicknamed 'islington-on-sea for a reason). My DCs love the place. crabbing when they were younger, sailing now they are older... Very easy to get to KC senior and almost as easy for the junior school. Best bus route in the area, too. One stop on train to fav to pick up high speed. But if you want other primary school options aside from KC then you may be limited.