I thought I had replied to this.
I dont know Lower Largo all that well but it is really central. If you go west it takes you to Leven. Now Leven aint pretty but it does have supermarket, a good play park and a swimming pool. Just before Leven is Blacketyside Farm where you can pick your own fruit. They also have a good farm shop and coffee shop. This year they have opened up a playpark with trapolines, zip wire and tractors etc. Across from this is Silverburn park. Further west is Kircaldy which again is dire but does have museums and art galleries along with some big parks. Ravenscraig park and Castle are meant to be good. Just along from that is Kinghorn which has a lovely beach and then Burntisland where you will find another indoor pool and a large funfair if that is your kind of thing.
But I would go East. Here you will find Elie which has a great beach where you can windsail. Cricket is played on the beach and you can walk over the rocks from Ruby Bay to a little lighthouse and an old bathing tower. Great spot for a picnic.
Leaving Elie there is another great farm shop which I would recommend you visit if you are selfcatering.
St Monans and Pittenweem are pretty little villages. Pittenweem has playpark and outdoor paddling pool and a chocolate shop.
Lots to do in Anstruther including the Fisheries museum, Life boat and the famous Chippy along with proper harbour and Marina. Go for sail to the Isle of May and see seals and puffins. There is a cheese farm on the back road between Pitenweem and Anstruther where you can visit the cows and see the cheese being made. Fantastic coffee shop there. Kellie castle is close to there but I have never been. Also in that area in the Secret Bunker(google) which my kids love.
Head north inland and Cupar has a lot going on. The Deer Centre is near here along and the Cairnie fruit farm which has a maze and all sorts. St Andrews has Sealife Centre, Golf Museum Botanic gardens, putting, ice cream shops etc. The Byre Theatre usually runs a very child friendly programme during the summer. Beach here is great for kite flying. Visit Fisher and Donaldson bakery for a fudgie!
If the weather is really bad then Perth and Dundee are under an hour away.
Throughout the summer each area/village will have gala days. The Anstruther Munster is great as is Pittenweem Festival. Check out the Visit Scotland website for the dates you need.