I wonder if Starfleet has an USS Illinois? I'd imagine the USS Illinois being a mid-to-late 24th century Starfleet ship of the TNG-era. It’s sister ships can be named after other states too, like the US Navy’s Iowa class battleships. We can hope the Starship Illinois doesn’t have several captains who were forced to resign or court martialed either while still captain or after promotion to admiral and spent time in a Federation penal colony (which isn't too far of a stretch considering some of the Admirals we’ve seen on-screen in TNG/DS9). The last US navy ship named USS Illinois was a pre-dreadnaught battleship at the turn of the 20th century. There was supposed to be an Iowa Class USS Illinois BB-65, but was cancelled.
http://en.wikipedia.org/wiki/USS_Illinois_(BB-65)
http://en.wikipedia.org/wiki/USS_Illinois_(BB-65)