From someone who works in DTA right outside Gate 1 walk gate...
For a CVW during a non-football weekend/non-parents weekend, I-Day/Annapolis Boat Show, parking on-Yard during the weekend will not be a problem, since staff and faculty will not be occupying spaces. If you get onto the Yard by 0730 on a workday morning, you can usually find space to park close in to Bancroft. Later it is, farther out you have to park, typically across the creek at Hospital Point. You can't park in front of the quarters on Porter Rd or in front of quarters on the Worden Field parade ground. Spaces you can park in are marked with a yellow painted triangle.
In DTA, there is a parking garages just off Calvert St., very close to the Church Circle end of West St. that the Westin is further down on. That's Gott's garage. There is another City parking garage just off Main St., reachable from Main St. or Duke of Gloucester St. I think the max is $20-$25 a day -- but both are brisk walks from the Westin. Actually, in the Metro DC area, $20 a day is relatively cheap.
I don't recommend parking on the street in Annapolis or the DTA area -- restrictions abound. The contract parking police are happy to swat you with a ticket, starting at $25 a day and going up 10 bucks every few days after. Historic district parking is especially fraught with danger.
I'd go for parking on the Yard with your DOD stickers and taking advantage of the hotel shuttle and have 'em drop you at Gate 1. There's taxi stand at the foot of Main St., so it wouldn't kill you wallet to take a taxi back to the Westin if the shuttle fell through.