There are plenty of train trips from Grand Central but the the prices though are expensive anywhere from Grand Central:
to 125th Street, the first stop on nearly all trains takes ten minutes and a one-way ticket costs $7.50 peak, $5.50 off-peak, if your leaving before 8:00pm your trip leaving Grand Central counts as peak, return is off peak. You could also take the Subway 4,5,6 trains (10-15 minute ride) up to 125th Street and Metro-North back arriving.
If you want a longer trip I suggest
the Hudson Line to Marble Hill ($8.25 peak, $6.25 off-peak, you can take the 1 subway train one-way) or Yonkers $10/$7.50, you'll get a taste of the scenery of the Hudson Line. If you time a round-trip right it will take less than hour costing.
Writing this post I'm reminded how much of a premium is placed on trip going to 125th Street or Grand Central (there in the same fare zone, the same price), a trip I almost never do. I live in Northern Manhattan and if I take Metro-North I always get on at Marble Hill or Fordham. New Haven to GCT is $20.50/$15.50 while New Haven to Fordham is $12 both peak and off peak (no difference for intermediate fares).
