The Sportsman in Seasalter and Jojo's in Whitstable are both AMAZING!!! Whitstable Oyster Company is good is you like seafood. And the Hotel Continental is good for a more relaxed atmosphere. These are my recommendations based on having lived near there 6 years ago. I know that Jojo's and Sportsman are still rated highly...not sure about the others but they were always good. have fun, Whitstable is great. Canterbury is not far and is good for activities...lots of history, some museums, good shops and restaurants.
Had a day trip, actually about three hours, in Whitstable last week. Had a coffee in a bistro / gastro type place, Samphire. Food smelt gorgeous, lovely menu and would definitely have eaten there had we been staying longer.
No idea on things to do with 9 year old am afraid but enjoy New Year!