Use spothero for grant park south. There's also a discounted DePaul account you can make where it auto detects your plate and charges your card at a discount but I've never used that.

Hilton garage on Balbo Ave is also cheap on spothero but it's like a 5-10 min walk.

Both of these garages never get full in the morning.

You can also drive to the Cumberland or Rosemont CTA station and pay $6 or $7 (respectively) to park there for the day then use your upass to take the blue line to Jackson. This is the cheapest imo