I hitchhike to the cliffs from in front of the Guilded Otter(a restaurant on Main St. in New Paltz, for the OP. It is a 7-10 minute walk from the bus station).
It's a spot that gives drivers time to see you and think about stopping, and also a safe place to pull over if they do stop.
On the way back, I go to the Overlook(a turn-out/parking area on the road in front of the cliffs, for the OP) and see if anyone is headed towards town. If not, or no one can provide a ride, then I hitch from the road just before the Overlook.
It's a little hairy because it's actually NOT a good spot for drivers to stop, especially if the Overlook lot is very full and they can't pull into it. Isually, the drivers do that, but last time a guy pulling a horse trailer stopped right there on the road, not giving a damn about traffic behind him.... I felt bad, but - hey, I needed a ride!
Question: IS it legal to hitch rides in NP? Last week I was in front of the Otter with my thumb out, and a car crested the hill. I said to myself "That looks like a cop car. But there's no lights on top..." So, I kept my thumb out and...it was a patrol car. Oops.
They didn't stop, either! But they turned right at the corner and I was like "Crap. They're circling around and I am going to be STUCK with no way to get to the cliffs once they tell me I can't hitch rides."
I prayed for the next car to pick me up and lo and behold, they did! Just as I was getting into the car, the patrollers swung back through. HA! I made it away!