There are overlapping laws that make things very confusing. An IL resident can travel THROUGH the state of Indiana with a handgun but not TO the state of Indiana with a handgun . . . as per the determination of the D.N.R.
Federal law protects travelers who are traveling through a jurisdiction. However if you are traveling to somewhere there is a potential problem. The D.N.R. has determined that Federal law does not protect someone who is traveling TO a range in Indiana but rather that the person must comply with INDIANA law. Indiana law requires a license/permit to carry a gun, and that includes transporting it to a gun range within the state. Therefore someone traveling from IL to IN to a gun range much be 'carrying' and therefore must comply with IN law.
Probably the easiest license to get that would allow a non-Hoosier to carry in the state of Indiana is the PA non-resident permit. Unlike the Utah or FLA permits, the PA permit does not require training so its quicker to attain but is far more limited than the other two popular permits.
But its legal for an Illinois resident to bring a gun to Indiana if that resident is staying in a hotel room in Indiana. Its not legal to remove it from the hotel room, except to continue a journey, or to return home.