If you have to travel any significant distance to get to Annapolis, the best football game is any game that falls on a 3day weekend in October. Go to the game then take the Mid into DC or Baltimore Saturday and Sunday. I suppose that there are Mids that get hugely Jacked up for games, but attendance is “Mandatory Fun” for Mids. When DW or I rolled into town my Mid wanted to "sleep in a real bed," order off a restaurant menu, take Mom’s CC card into bed-bath-beyond, shop for snacks at Whole Foods and watch PPV from a hotel bed with her Mom-n-Dad. Football games are fun for them, but its something they do most weekends in the fall and they really don’t get to sit with you much. In contrast that 3rd day of a Three day weekend is golden, you can give the Mid a real break from the Yard.
Having said that, I was lucky to be able to attend 7 games while DD was there. USAFA was always a great games to see. A really good substitute for ARMY/NAVY which I’d hold off on until after your Mid graduates. You just don’t get to see your kid at all at that game. Mids have to travel in for the game as a group and they have mandatory stuff to do before and after the game. It really is a “Hi Mom-Bye Mom” situation. You'll get much of the same SA rivalry vibe at USNA / USAFA and some time with DD/DS. Go to Army/Navy after graduation. You’ll get to have a great time with your DS/DD and they can pay for the tickets!!
I see that Columbus Day weekend is a Bye for Navy this year, too bad………. Not really, my DD would have been cheering the fact that she could leave the yard and head into DC without losing half of Saturday to a football game. We love, (well..loved) college football in my family, but while DD was a Mid if DW and/or I were in Annapolis seeing a good game was very subordinate to giving DD a break from the grind.
I had great luck with Stub-Hub and Seat Geek (there are a bunch more sites these days). I always found better selection of seats at better prices vs purchase through the Navy sources. I’d look for tickets about 4-6 weeks before the selected game, (season ticket have to decide if they are going or selling). I kinda felt like I was sending my money into a black-hole at times, but over 7 games, the tickets I was delivered were the real deal and exactly what I had ordered.
I found that the best seats were visitors side across from the Mids. Never was able to get really good seats on the home field side.
Good luck to you.