You can file your claim in your 'home' court, but the Defendant will have to be served with notice of the suit in FL. He will then have the option of filing a 'no jurisdiction' response claiming that the IL court has no jurisdiction or to ignore your notice entirely. If he ignores your notice, you will receive a default judgment against him. However, that court judgment can only be used to seize assets that the debtor has in IL. If all their assets are in FL, then you will have to domesticate your judgment into the FL legal system (necessary to use the FL enforcement process). Then, if the judgment is recognized in FL, you can proceed with post judgment enforcement (garnishment, seizure, levy, etc.).
Or, you could file your case in Federal court.
All in all, not a cheap or simple process, which is why any interstate purchases have a larger amount of risk.