Hey Brandon,
Yes, there are plenty of places to eat around the hotel and because you'll have a car you'll be in good shape. There's a deli, don't recall the name, but if you turn left out of the hotel parking lot (hotel is behind you) and drive for a few miles it will be on the right, think there's a little strip mall there too. I think you'll pass Friday's (which is on the left) before getting to this deli. Anyway, they make FANTASTIC sandwiches and had lunch specials etc...
Then of course there's the Friday's and if you turn right out of the parking lot there's a Burger King down that way a couple miles, I think it's on the left. There is also a diner, The El Dorado, which used to be great but the last Tarrytown Fest we ate there and it was gross. But maybe they were having a bad day though. Just ask the hotel staff, they'll be glad to guide you. The good thing about Tarrytown is it's a small burg and it's easy to find stuff. In fact, ppl will tell you something's "just down the road a piece'!
Hope this info helps some.