JHancock

Big Bend is an excellent park to "get away" from people. My recommendation though, try to go in late August, early September, when school is back in, and camp in the middle of the week. You'll have plenty of land to yourself.

My girlfriend and I went last year in August and absolutely loved it. We went in August, and at one point during the week, only three of the sites were occupied, including us.

To get even more seclusion, hit the backcountry. We hiked out the Laguna Meadows trail about 6-7 miles to the South Rim and set up camp there for a night. The backcountry sites are great. They're well spread out, 1/4-1/2 miles between sites, but you'll likely be the only one out there anyway, and each site is equipped with a bear box to store food in. We had deer come within 10 feet of our tent that afternoon. The next morning, we hiked back through boot canyon, another 6-7 miles. We didn't see anyone else from the time we left the parking lot til the time we got back.

There's several other parks around the state that offer backcountry camping if you're into it and want the seclusion factor. Caprock Canyons is another one I'll be doing in September for three days and two nights.