I plan to visit with my family so train tickets would be quite expensive. Where should I park the car once we get there?
I don't quite understand your question.
Are you driving to Cold Spring to visit family? If so, then park at their place.
Or, are you driving to the train station in Cold Spring, getting on a train to go visit your family somewhere else? In that case, just park at the station.
Or....are you driving to NYC and taking a train to Cold Spring during your stay and you want to know where to park the car in NYC while you're in Cold Spring?
If you are driving to Cold Spring, you can park almost anywhere overnight. During the day some areas are four hour parking so watch the signs. If snow is expected, you need to either park in the municipal lot or at Kemble and Boulevard in the winter parking area.