Some thoughts as a Chicagoan:
The location of the Chicago HGVC is in the eastern part of the Streeterville neighborhood. There are plenty of bus stops in the neighborhood but if you want to take the L (which I strongly recommend over buses) it's going to be a 15 - 20 minute walk depending on your ground speed. Why I would recommend the L over busses is a different conversation but suffice it to say the L is much faster to get around and can get you close to everywhere you want to see if you're visiting Chicago.
Like NYC, Chicago is a walking city. As a rough guide, expect a 5 - 10 minute walk from the L to many places you want to go. The Shedd / Field Museum are closer to 15-20 minute walks from the closest L stop but there is nice walking path. Paying for 4 riders on public transportation will change the economics and may not be that much cheaper than taking a cab or rideshare especially accounting for the time involved.
Like
@ljmiii said - parking costs are no joke in Chicago. You may be able to find street parking within a few blocks of where you want to go but downtown parking has been crazy expensive ever since the parking meters were sold off. Not to mention that it's a PITA to drive around and park in multiple locations.
If you don't plan on taking your car in and out after arrival, consider parking through SpotHero. You should be able to get a spot in a neighboring garage for much less than $62/night (I'm assuming that is before taxes?) FYI - Chicago is the only big city where you can get from either aiport to downtown for $5 (from ORD) or $2.50 (from MDW). So if you get cheap tickets and don't want to drive and pay for parking, you can get downtown from the airport inexpensively and fairly quickly using the L.
Safety has been a concern the past few years. While the Streeterville neighborhood is amongst the safest in Chicago, serious crime can and does occur in all the neighborhoods nowadays. It's a big city, take precautions and keep your wits about you (especially after dark) and you'll be fine.
Cabs are exempt from a car seat requirement. Technically, Uber / Lyft are not exempt but I have never had a rideshare driver decline a ride because I was with my kid and didn't have a car seat. Highly recommend downloading the Curb app before you come to Chicago if you plan on taking cabs. It's like a ridshare app in that you can hail a cab and know the fare ahead of time - with the bonus that there is no surge pricing.
Regarding carseats: I haven't used the folding booster that
@bizaro86 mentioned but I did pull the trigger on a RideSafer travel vest. Depending on your child's age and weight, it is an alternative to a car seat or booster (the manufacturer states that it is a certified alternative to both). It's so much easier than lugging around a car seat, I am very happy with the purchase every time that we travel.
Finally - have a great time! Chicago is an amazing place to visit and there is so much to see and experience. Not to mention the amazing food scene! Literally every person I know who has visited has been blown away by the city. Enjoy your trip out here!