Some of BA's LHR lounges have play areas for children. Very few other airlines have lounges except perhaps at their hubs with such features.

While it's not common to have such child-friendly lounge facilities in most airline lounges, some airports have designated play areas for children in some part of the airport and no airline lounge access is needed for them: MSP, HEL, WAW are some such airports.

Even some small segment of regional airports in the US have a play area for children, but that's more of an Upper Midwest feature at a very, very limited number of airports than it is a common feature in the US. European airports seem to be sort of ahead in this game. Asian airports are generally more lousy in this regard despite the much higher proportion of youthful populations than is the case in Europe.