The home state of Scooby and the Gang isn't directly identified in the animated Scooby shows and movies. However, the state is revealed in the live-action TV movie Scooby-Doo! Curse of the Lake Monster.
Ohio as Scooby's home state is utter nonsense, because Ohio's topography in no way matches the topography featured in the first season of Scooby Doo Where Are You!
According to the topography revealed in those episodes, Scooby's home state could only be Texas.
One episode shows the Gang going into the USA's desert southwest, a part of which is in Texas.
One episode shows the Gang visiting the only lodge that Fred could find that had enough snow for skiing. The Guadalupe Mountains National Park in Texas could be the location of that lodge. "Since Guadalupe Mountains National Park is home to the highest point in Texas, Guadalupe Peak at 8,751 feet, there is a chance you’ll see this spot covered with snow throughout the winter."1 - tripstodiscover.com
One episode shows Fred accidentally driving the Gang through a swamp that has alligators. Brazos Bend State Park in Texas has swamps and alligators, too.2
One episode reveals that Scooby and the Gang live near a sea port. Texas has sea ports.
Indeed, Texas is the only state in the USA that has all of the above-cited features.
Portraying Ohio as Scooby's home state makes as much sense as portraying Fred with brown hair.
Oh, wait. Fred is portrayed with brown hair in the live-action TV movies Scooby-Doo! The Mystery Begins and Scooby-Doo! Curse of the Lake Monster.
Go figure.
Information Sources:
1https://www.tripstodiscover.com/best-places-to-see-snow-in-texas/
2The Texas Swamps. The Lone Star Untamed https://thelonestaruntamed.wordpress.com/2015/02/15/gator-bait/