First things first – the Empire State Plaza is an exceedingly uncomfortable place to be. Aside from that, it has enough history and culture to keep a family interested for an afternoon. The New York State Museum with free admission is the only museum in town worth a visit, but it’ll tie you up for a good hour.
The rest of the day will be spent getting lost under and on top of the Empire State Plaza before you retreat, tired and defeated by inhumane architecture, to the old downtown around where Fort Orange used to stand. The fort was built by the Dutch East India Company and the land is now used by the State University of New York’s administration building.
You’ll be done by lunchtime, then you can move on to another city like Springfield, MA or Hartford, CT.