Hello Sophie, I'm not too familiar with Burntisland, maybe calums mum would be as she is a bit closer than me, but I know there is a nice beach there. There are pretty good train links too I think. There is Beveridge park in Kirkcaldy, not too far by train or car, there is a bouncy castle , putting green etc there. There are a couple of indoor adventure play areas quite nearby, can't remember the names but I'll do some research.
I can't think of anything else at the mo, will get back to you though
x x x x