Most of the major hotels, especially in midtown, will be able to advise you on how to get to whatever sites you wish to see. Manhattan may be regarded as divided into east and west sides by Fifth Avenue. The A, 1, 2, and 3 subways run on the west side; 4, 5, and 6 on the east.
Not all worthy locations are in Manhattan, which comprises only 21% of the land surface of NYC. Each of the 5 boroughs, for example, has a zoo your children might enjoy as each specializes.