The U.S. is daunting, but I'll throw out suggestions for each state where I can think of any. Some of these can be used alternatively for different states, I'm selecting somewhat arbitrarily. I am not familiar with a lot of these.
Alaska - Cabela's Big Game Hunter 2012
Arizona - Postal 2
Arkansas - Redneck Rampage
California - True Crime: Streets of L.A.
Colorado - Super Columbine Massacre RPG!
Connecticut - Deadline
Florida - Hotline Miami
Georgia - The Walking Dead
Hawaii - Shakedown: Hawaii
Idaho - Boise: the video game
Illinois - Michigan: Report from Hell
Indiana - Indianapolis 500: The Simulation
Kansas - Gun
Kentucky - Kentucky Route Zero
Louisiana - The Adventures of Bayou Billy
Maine - Still Life 2
Maryland - Fallout 3
Massachusetts - Assassin's Creed 3
Michigan - Deus Ex: Human Revolution
Mississippi - Left 4 Dead 2
Missouri - Square's Tom Sawyer
Montana - Custer's Revenge (I'm reaching here, but Little Bighorn is the battle most associated with General Custer and was fought in Montana)
Nevada - Vegas Stakes
New Jersey - Jersey Devil (cheating a bit here)
New Mexico - Half-Life
New York - Spider-Man 2
North Carolina - North & South
North Dakota - Where in North Dakota is Carmen Sandiego?
Ohio - Shivers
Oklahoma - Nancy Drew: Trail of the Twister
Oregon - Life is Strange (at least I'm not giving you guys Gone Homo instead)
Pennsylvania - Ultimate General: Gettysberg
Rhode Island - Eternal Darkness: Sanity's Requiem
South Dakota - A Mind Forever Voyaging
Tennessee - Destroy All Humans (Turnipseed Farm)
Texas - Call of Juarez
Utah - Freekstyle
Virginia - V-Tech Rampage
Washington - Alan Wake
West Virginia - Fallout 76
Wisconsin - The Vanishing of Ethan Carter
Wyoming - Time Crisis 4
The following state I couldn't find anything for or couldn't verify that what I found was actually set in the state that was claimed.
Alabama
Iowa
Delaware (I wouldn't be surprised if one or more games about the American revolution includes it, I just couldn't find it as the actual definitive setting in one)
Minnesota
Nebraska
New Hampshire
South Carolina
Vermont