7x9 foot tent on a mountain?

Hey everyone. My girlfriend and I will be hiking in the Indian Lake area this August on various mountains (Pillsbury, Snowy, etc). We will most likely be spending the night on the mountains somewhere off the trail near the summit. The only tent we have available is 7x9 feet, and she is insisting we stay in a tent instead of hammock. As someone who is unfamiliar with the denseness of the Adirondack forest and mountains, do you think we will be able to find a 7x9 foot spot for our tent somewhere on the mountain. I am sure we would have to bushwhack a little and clear the forest floor.
Thanks!