Every home football weekend is crowded, a snick or two under Commissioning Week, I-Day, PPW levels. Hotels fill quickly.
The annual Fall Boat Show fills the town to overflowing for two weeks in October.
Plebes have town liberty after the game ends. They sit with the Brigade and are in a duty status until after Blue and Gold is sung. They normally have to be back at a set time that night. There is the possibility of an "overnight" being announced at the game itself. If your DS does not have the duty that weekend (he should know his duty schedule just before start of ac year), he can be out in town. Sunday, he can see you on the Yard.
Sep/Oct games have the best weather, and the town will be crowded with reunion classes, which happens at every home game, not just the dedicated Homecoming game. Nov games can be chilly and rainy.
PPW does give the plebes a whole lot more time off-Yard (parts of Fri, Sat, Sun, no overnight, typically) and their first real break since I-Day. They also don't have the stresses of ac year yet.
Pick the wrong fall football game prior to an academic reserve period, and DH may tell you he won't have time to get anything done on Sat since he was with you and had the game, so he has to spend Sun getting a paper done, doing problem sets, prepping for a lab or studying for 6-week exams, and can't see you except for a lunch break on Sun if you bring him Chipotle. You can see the ac calendar on the USNA.edu public calendar site.
If you don't go for PPW, rest assured, someone will take pity on him and get him off the Yard. He will have met his sponsor family the previous Sunday. We rescued many a plebe whose family didn't make it. A roommate's family may adopt him.