You know how they never tell you what state they are in, but they like always try to make you guess what state they are in? Well I finally figured it out! They live in Utah. Here's my reasoning, you know how Jebediah Springfield led all the pioneers to Springfield? It's just like Brigham Young/Joseph Smith leading the mormons to Utah. Also there was a halloween episode where all the dead people came back, and one was Butch Cassidy, and I'm pretty sure his hideout was in Utah, and he died here.
Also remeber that episode where they are casting fallout boy for that radioactive man movie? When they are looking for a place to film there's a huge ad that says FILM UTAH, and they say something like "Thats it!" then point right next to it and it says film springfield. Also there's another halloween episode where those 2 alien guys come to the simpson's house, and homer says "great.. mormons". And there is a town Utah actually called springfield (it might be springville actually I'm not quite sure), also the town next to springfield in the simpsons is called ogdenville, and there's a city here called ogden. Yeah, this is just my specualtion, what do you think?