You're talking about the FOID card? It is only issued to Illinois residents. The good news is that it is only required of Illinois residents to own a firearm or buy ammo. If you are a non-resident you can transport a firearm, encased unloaded and not immediately accessible, or broken down, or buy ammo without it. It is also legal to have a loaded firearm in your "abode", which HB182 that passed this year clarifies is a hotel or motel room.
You can look at the transportation rules at www. isp.state.il.us Keep in mind that local ordinances may be more strict than state law. If you are traveling in the Chicago area, or north of Interstate 80 this may be the case. If you follow federal transport laws you are OK there as well.