Schoodic is on the next peninsula to the east, so you have to go back into Ellsworth and take US Route 1 north to get there. Watch for signs for Winter Harbor. Great place to take a picnic lunch, beach chairs, binoculars, and a book; but don't expect to get it once you've gotten there. Not nearly as crowded as on Mount Desert. It looks straight out to the open sea, so (as always) take a jacket along if it's an on-shore wind.
As for us, we'll be at Schoodic Point tomorrow. We're camping at Timberland campground in Trenton. We couldn't find anything at Bar Harbor campground (no sites available after an hour of riding around).....but we're happy here. At the moment there's a country band playing and it's kinda fun.