As to where to donate it the first thing to do is to talk to the museum first to see if they want it.
The Smithsonian is offered countless truckloads of 'stuff' every year by well meaning people but the Smithsonian rarely accept anything anymore unless it is historically very important. The reason is they have no place to store it and little room to display things. Everytime they accept something it costs them money to build a place to keep it and to manage it into the future. If you offer them an original SPAD they will say yes, or
Eddie Rickenbacker's original uniform they will say yes, but once you get beyond things like that they get very picky about what they accept.
Smaller and less famous museums are a bit less picky but they are under the same constraints as the big museums in terms of having to pay for the annual upkeep of whatever they take in and have a building big enough to store it in. They find it very hard to raise money for such costs and so they are usually hesitant to accept contributions of anything but cash.
If you do find a museum that would like to have these, you will then need to be fully aware that once they are given there is no assurance they will ever be displayed. Also you need to know that they have the right to 'deaccession' anything that has been given to them. What that means is they can and do sell off or trade away things that they no longer feel are essential to their collections so they can get cash to pay for their daily operations or to get things for their collections that they really want.
I think giving the really historical things to a museum that will honestly treasure and display it is the way to go for that class of artifacts, but that finding a committed collector who will care for the more common things is the best way to go. These shell casings are nice, but I would not put them in the really historical category so you might be best talking to smaller museums that are not on the financial brink (some smaller museums are struggling and they can and do go out of business from time to time and their collections are auctioned off), or talking with committed collectors.