I went by bus. Coach USA (Short Line Bus) offers day packages to Storm King, leaving from the Port Authority Bus Terminal, that includes transport and ticket. I totally recommend it!
Once you get there you will enjoy the great art pieces in the middle of the nature. My experience was in sommer. If you don´t have any other option, take sun protection! But if you can choose other season, fall ist the best time to visit it. The Hudson Valley get amazingly coloured during the autumn.
Go and visit it!