Firstly, have fun! That's awesome you're gonna see the first race here!
If you're staying inside the city limits, you won't need a car. Take CTA and buy a daily or weekend pass.
Lou's is one of the most popular deep dish pizzas, but it's my least favorite. Pequod's is where my heart is, but you'll need a reservation or face a 2 hour wait. Chicago Pizza Oven Grinder Co is unique, and their Mediterranean bread is amazing, but also a major wait (and cash only!)
Take a walk on the lakefront path. It's open all night for walking/running and biking.
Chicago is a city of neighborhoods, so few actually hang out "downtown" after work. Some people live in the Loop, so they do. Things shut down early there. Many neighborhoods have a "main area" that rivals other cities downtowns.