In Texas there's no site-specific ressies. You DO get to pick from what's available when you're in the office. However, once you "pick" few parks will suggest/let you get another site you feel is better.
If they do, it involves driving BACK to the main office, possibly standing in line AGAIN, and after those 5-20 minutes have passed you're likely to find the spot you wanted is GONE now, thus repeating the process all over again.
I HAVE driven around the park & found 4-5 sites to pick from, but still have to go back to the main office so I can get the proper paperwork to display on my windshield. Towing a trailer -- it's not my favorite thing to do.