It took us what seemed like the better part of the day. If I remember correctly it was about 2-3PM when we checked into the hotel and we left early in the day. It was slow going through some parts, and it did seem like we would never get through NJ; I remember a number of stops there. It was a last minute decision for us one weekend and we had no idea how the system worked so I am not sure if some trains are faster or more direct that the one we used.
We lived in Alexandria, VA, about a 25 minute ride on Metro to the DC station, then to(I think it may be Penn station) in NY. I cannot even remember what we paid in 1998. Overall I think it is not as fast as driving but there are also no parking concerns and I think the hotel was $60.00/day for limited parking.
We drove one time to the Princeton, NJ station and paid around $12.00 each to get downtown NY, but this also took a good part of the day from the DC area.