I will have a rental car for GenCon, but am looking at $20 a night. If I don't plan on using the car, perhaps I can find some cheaper parking lot somewhere and take an Uber to it? Possibly free?
I'd suggest getting a rental car to the convention and then turning it in. When you're ready to leave arrange for another rental to wherever you're going.
Gate Ten still has 5 day (Wed-Sun) spaces available at $16/day. They have shuttles to the Con & 24 hour in/out access. The lot they still have available is a bit far (about 1/2 mile?) from the ICC though, but if you're just leaving the car there, not an issue.
As brooks said, if you're not going to use the car, why spend the money keeping it in a lot for 4 days? Turn it in when you arrive, get another when you leave.
It actually costs more to turn in and rent again. One way rentals are expensive. It's rather absurd, tbh.
Normally, the rental company might not find out, but if anything happens, ticket/fender-bender/etc., they’ll get notified and you could be on the hook for the full cost and penalties.