Watch noon meal formation if it's scheduled. Go to USNA Museum; visit John Paul Jones in the crypt. Sit in the peace and quiet of the Chapel and enjoy the Louis Comfort Tiffany windows. The Visitor Center usually has a self-guided walking tour brochure hitting the high points open to the public.
For an inexpensive lunch on the Yard, go to the Drydock in Dahlgren Hall, open to the public and a small walk from Gate 1. Grill items, deli sandwiches, pizza. The Muhlheisen!
I took a quick look at navysports.com to check for any events, but didn't see anything on the Yard. Seasons are wrapping up, or teams are traveling. You might see some intramurals going on.
In DTA, it's worth the block or two walk up Main St. to get a milkshake at Chick 'n' Ruth's Delly (local spelling) or a Walkie Cup at Annapolis Ice Cream Company.
Find a bench by City Dock and people-watch and boat-watch.
There's a Starbucks for wifi, as well as other places.
I used to race sailboats out of Annapolis and often we'd have the USNA boats in the races. Annapolis is a great little water's edge town and I am excited about going back. I wish DD enjoyed sailing like I did.