RE: Aberdeen Proving Grounds- They had an excellent museum, but military downsizing has closed the museum, and all the artifacts are being relocated to a new museum to be built at Fort Lee, VA. Completion is several years off, at best, and if military funding continues to be slashed may never come to pass.
The National Rifle Association “National Firearms Museum” in Fairfax, VA (Washington suburbs) is one of the best in the country in terms of arms. Also the Fraser Historical Museum in Louisville, KY. Each is worth a half day, and are very well done. Cody Firearms Museum at the Buffalo Bill Historical Center in Cody, WY- a bit out of the way (okay, a LOT out of the way) but absolutely superb with four other great museums in the same building. Half day minimum, but an easy day or two if you have the time.
For military ordnance, but not small arms the Hawthorne Ordnance Museum, about 100+ miles from anywhere has truly incredible stuff, but it is really remote, somewhere just short of the edge of the earth. Too bad, but if you can arrange it, well worth a stop for ordnance enthusiasts.
The Army’s Artillery Museum at Fort Sill is superb. Springfield Armory in Springfield, Massachusetts is wonderful. The American Precision Museum in Windsor, VT is a chance to visit the building where many historic arms (including many Sharps) were made and gain insights into the “American System” of machine tools and interchangeable parts. The Remington factory in Ilion, NY, offers tours of the factory on a limited basis so call in advance. The Air Force Armament Museum at Hurlburt Field, Ft. Walton Beach, FL, is pretty much weapons and ammo related, and the Naval Aviation Museum at Pensacola is only about 50 miles away. U.S. Military Academy Museum at West Point, NY is excellent.
Of course, the best ammunition collection in the country, and probably the world is at Woodin Labs in Tucson, AZ, or so I am told.