Happy to advise you but I would have thought your family in Pittenweem would be the ones to ask. Crail and Anstruther are also nice wee towns close by or you could go further afield and base yourselves in St.Andrews. Its very walkable with a buggy/pram for your baby although some of the cobble stones can be a bit bumpy!
The above website may help you for the East Neuk and the next one for St.Andrews
You don't say what time of year you are visiting but I am assuming its NOT the middle of winter!
In summer accommodation in St.Andrews can be pricey. If that is a factor and you are on a budget you will probably be cheaper in one of the coastal villages - there is also St.Monans and Elie to choose from which are equally good, as well as Kingsbarns further round towards St.Andrews which has a lovely little beach