Rye - recommendations for food, activities in or nearby

[babydriver]

Hi, we're off to Rye for a week from Friday. What would MNers recommend - we've a 3mo old and a 3.5 yr old.

I know about camber sands, the dungeness and Kent& East sussex railways and Bodiam castle. What else is good for kids?

Also, any eating recommendations? And is there a good supermarket or farmers market or local shops nearby - I seem to remember the Budgens being pretty useless.