Trish drove us here with the help of the GPS. Alright this isn't true, she knew exactly where to go. You do need to drive to Sleepy Hollow if you live across the river, otherwise you have to take the train to the city then back up and get a cab or make a really long walk.
The best two ways to get to Sleepy Hollow are to drive or to take the Metro North railroad. If you opt to take the railroad, be ready to do some walking or take cabs to the various points of interest. All things considered, I would advise renting a vehicle or taking your own depending on the circumstance.
If you plan on making a day out of touring the various places in Sleepy Hollow that are of interest, you really should have a vehicle. Most of the places are spaced a half mile or more away from eachother. You may be able to make due with a bike, but I definately wouldn't suggest walking it.