The Tri-State Area is the name of the metropolitan area surrounding Danville. It was founded by John P. Tristate, who united the Bi-State Area with an adjacent area, founded by Otto H. Adjacent. Tri-State Area Unification Day is celebrated on July 15 ("Hip Hip Parade").
Roger Doofenshmirtz is the current mayor of Danville. His brother, Heinz Doofenshmirtz often plans to create chaos in this area, not just the city of Danville itself. For such purposes, he once built a "Plush" scale model of the Tri-State Area.
Some businesses and groups have "Tri-State Area" in their name (e.g. Tri-State Area Public Library, Tri-State Bombers, etc.).
While describing one of his schemes, Doofenshmirtz used a magnifying glass in front of a map of the United States to reveal the Tri-State Area's location. The magnifying glass was positioned near the Denver, Colorado area, which is within driving distance of Mount Rushmore ("Flop Starz", "Candace Loses Her Head").
One scale model by Heinz Doofehnshmirtz depicts a geographical area of less than one square mile. However, another larger scale model was made by Doofenshmirtz; the scale of the model is unknown ("Toy to the World", and "That Sinking Feeling").
Series creator Dan Povenmire has stated that Danville is not in any specific geographical location. The surrounding region changes to fit the needs of the episode's story, leading to Danville and the Tri-State Area being near both Mount Rushmore and the Atlantic ocean at the same time.
The Tri-State Area may be based on Toy Story's Tri-County Area.
In the real world, a tri-state area need not encompass whole states. For example, Chicagoland includes several counties in northeast Illinois, along with a few in the most northwest part Indiana, and one in the most southeast part of Wisconsin.
There is also a Quad-State Area where the Regurgitator's base is located. It is mentioned while Major Monogram is briefing Agent P during the beginning of "Oh, There You Are, Perry" Other than the fact that The Regurgitator had built his base here, not much is known about the Quad-State Area. Most likely, it is located on the border of Utah, Colorado, New Mexico, and Arizona. So far, it has only even been mentioned in the episode "Oh, There You Are, Perry". Judging by the fact that Doofenshmirtz drove there in such a short time, it is most likely close to the Tri-State Area.