Although from the East Coast, the Griffins appear to be arriving in Columbus, OH from the west as I-70, the main east-west thoroughfare through Columbus passes to the south of the downtown area.
Located to the North of Columbus and not in the downtown area, the Columbus Zoo and Aquarium does feature the only permanent roller coaster in central Ohio, the 1956 PTC coaster now called the Sea Dragon.  Recognized by the American Coaster Enthusiasts (ACE) as a classic coaster, it is one of the very few surviving roller coasters still operated with hand brakes.
The name of the park the Griffins travel to is "Six Flags Columbus". The area of the Columbus Zoo the Sea Dragon is located in was once named Wyandot Lake, which was previously owned by Six Flags. 
The Wilhelm Scream is heard when the roller coaster crashes due to Peter's weight.
Six Flags Quahog features a roller coaster known as The League of Extraordinary Gentlemen: The Ride. The League of Extraordinary Gentlemen is a superhero film adaptation loosely based on characters from the comic book limited series The League of Extraordinary Gentlemen by Alan Moore. It is an action adventure film set in the late 19th century, featuring an assortment of fictional literary characters appropriate to the period, who act as Victorian Era superheroes.
The items that Quagmire "eats" are Honey, Peaches, Ginger, Candy and Olive until he realizes he isn't looking at a list of foods but of girls.
The uncensored version of this episode includes Peter criticizing Jim Davis for writing Garfield: His 9 Lives, particularly the segment "Primal Self", in which it is implied a previous incarnation of Garfield kills an old woman.