If they have a car, they could also drive down to Poughkeepsie (about 1.25 hours) then take the Metro North train down to Grand Central. I think that works out to be quite a bit cheaper. Amtrak looks to be about $90 round trip and the Metro North is about $25 (off peak) and they have large discounts for kids. Metro North also typically runs more trains than Amtrak, so there's more flexiblity in the schedule, especially if you stay late.
Metro North Schedule & FaresThe trains aren't as nice as Amtrak's, though they are clean and well maintained, and you do have to drive the hour from Albany, but it does save a significant chunk of change. I think it ends up taking a little bit longer than if you take the train straight from Albany, but not by much. Just be sure and buy your tickets at the station or on the web. They hit you with a surcharge if you buy on the train. They have machines at the stations that are very quick to use.
I would also suggest getting a metro card so you can use the subways and busses when you get there. You can get them at the machine when you buy your ticket or at Grand Central. The subways and busses are the most efficient way to get around the city, IMHO.
Mike