Whitstable, great for crab fishing, two pebble beaches, the harbour has a real buzz at the weekend and has open air cafe, craft huts and retail sheds. Some good fish resturants but stupidly expensive. The weatherspoons in whitstable is cheap and new, not rough and full of pissheads like others. There is a good playground in the castle grounds on Tower hill, but it really only any good for under 8s (free though) There is a cafe in the castle (expensive) so you will be better crossing the road to the tea gardens. The town is good, but it is PACKED at weekends so visit in the week if you go. Other good beaches are broadstairs and the bays between there and Margate. Margate is great too, the old town is fab and there is the Turner Gallery - free :) Lots of arcades and the rest of the town is pretty run down but its up and coming. Tracy Emin was rumoured to have bought one of the flats in the high rise (you can't miss it). Id make a passing through visit to margate, not plan a whole day - broadstairs is my favourite beach, it does get packed but its great and you can walk just around the bay and find deserted beaches.
Bedgebury is a loooong way from faversham (over an hours drive) but it IS great there. It also has go ape if you are mad brave, but that is EXPENSIVE. There are quite a few nice woodland walks between whitstable and canterbury., those are free, however no playgrounds! Thornden woods has woodland art and sculptures on a circular walk, free but the car park is a bit small.
Rochester is good - the guild hall museum is excellent if your kids are into boats as it is done out inside on three floors like the inside of an old boat - and its FREE to get in. Rochester castle good, you don't have to pay to walk around the grounds, not really worth paying to go in castle as its just a shell, and bloody high!
Just outside faversham is Oare Gunpowder works - its more interesting than it sounds, again, free! here definately worth a visit, would be a half day visit which you could look around faversham town the rest of the day - LOTS of pubs and id avoid the weatherspoons (RAF - rough as Fuck!) it is the home of the oldest brewery in the country, where they brew spitfire, so if you like beer......
Most of the zoos are really pricey because they sell mainly on yearly tickets. If i were to choose one, id choose Wingham Wildlife park (outside canterbury) as its not too big, can get up close to the animals and even handle the snakes and spiders, which the kids always love.
Canterbury is worth a visit, there is the cathedral but you have to pay to go in. It is a NIGHTMARE to park though and parking is stupidly expensive. There is a cinema which has cheap showings at 11am every day of the holiday (£2.50 per child adults go free) if it rains. There are a few museums in canterbury, not sure about the entry prices.
Dymchurch and new romney are great, id recommend the light railway which will take you to dungeoness, nuclear powerstation - you can visit (or at least you used to be able to) and its cool, although a bit disturbing when you have to be tested for radiation, id avoid if pregnant. Dungeoness beach is defiantely worth a visit its desolate (or at least it was) but now many of the fishermens huts have been turned into homes of some archetectural interest. Some people converted railway carriages. It is a long way from faversham though so im not sure id bother if i were only visiting for a few days - its over an hours drive.
Im sure i'll think of more places :)