DC is not part of Maryland or Virginia so they wouldn't be under the laws of those states. That doesn't apply to other areas-
Rules and regulations for Fort Benning, Georgia (a United States military installation)
5-2. Vehicle traffic laws.
a. Reference AR 385-10, AR 190-5 and MCoE Reg 190-5.
b. General.
The traffic laws of the State of Georgia and the State of Alabama apply on to respective lands of the Fort Benning military reservation (see Title 18, United States Code, Section 13 and Department of Defense Directive 5525.4). All persons who drive a motor vehicle on Fort Benning are responsible for complying with State Laws. (p.7)
5-14. Alcoholic beverages and beer.
a. General. The sale, possession and consumption of alcoholic beverages and beer on this installation is governed by the provisions of AR 215-1, Chapter 10.
b. Consumption of Alcoholic Beverages. Consumption of alcoholic beverages by military personnel on duty is prohibited except where specifically authorized, in accordance with MCoE Regulation 210-65.
c. Purchase, Possession, Consumption of Alcoholic Beverages.
All personnel at Fort Benning must be 21 years of age in order to purchase, possess, and/or consume alcoholic beverages on Fort Benning. This is the law of the states of Georgia and Alabama. Positive proof of age will be determined prior to sales. Bona-fide guests may purchase alcoholic beverages by the drink if they meet the Fort Benning age requirement, but may not purchase in bulk. (p.12)
http://www.benning.army.mil/garrison/content/pdf/MCoE Reg 210-5.pdf
The address of the installation is Fort Benning,
GA 31905.
Why?
It's part of Georgia.