The pilgrims' original destination was not New England but the Hudson River (around where New York is today). After being battered at sea by storms, thrown off route several hundred miles, and with low supplies, they made landfall. They could not sail farther south because they lacked supplies and the moral. They also did not anticipate New England having bad weather. Since Massachusetts is 600 miles south of London and on the same longitude as Madrid, they actually anticipated a Mediterranean climate when they arrived. source edit: extra word

Since no one has done this yet, let me issue a gentle correction to one of the assumptions in your post:

The entire country was open

Actually, the area where the Pilgrims settled was fairly open, as the local native American tribe that generally lived there had been recently decimated by disease and intertribal warfare. (The Pilgrims plundered several native graves, looking for grave goods and/or food that they thought may have been interred with bodies.) But the area around Plymouth, and in fact much of the continent, was populated by Native Americans; had it not been, and had it not been for help from them the Plymouth colonists would not have survived.