I havent lived here long! We tend to take our two children to most places, just ask when we go in.
The Punch tavern, Herne Common is a family pub
There is a Brewsters in Margate
We have been to Wetherspoons in Both Herne Bay and faversham without problems
The Beefeater at Whitstable is good with the kids aswell
But as i say most places are ok