you could take the 1 train to 14th or then hop the 2,3 to 42nd and then connect to grand central. On weekends, you may have some difficulty if they are doing track work. I would suggest an application for your smartphone called nycmate (this is not an advertisement). It lets you know what trains are running with delays. You will be in moderately close walking distance to a number of subway lines if your usual subway line is delayed.
Hello Pj, you should have no problem. The total distance from start to finish is approximately 2.3 miles. By subway it should take about 20 minutes including the walk from your home to the train station.