No car needed. Take the train (the Orange line) to the Clark/Lake stop. It's the only train that runs from MDW to the Loop. When you get off the train, look for the walkway bridge that crosses over the tracks to the other side of the platform. Use that bridge to cross over to the other side of the platform. Wait for the Brown line train. Take it one stop to Merchandise Mart. (You'll cross over the Chicago River right before you get to the MMart. If you're facing fwd in the train, yOu'll see your hotel off in the distance to your left, but the real view is to your right).
When you get off at the MMart stop you'll want to cross back over to the other side of the paltform. You can then go inside the Merch Mart and walk through the bldg (the building is enormous - it's at city block or more so it'll take you a few). The hotel is across ths street on the west side of the MM.
If my descriptoin sounds confusing, don't worry. It's easier than it sounds. Trust me.
"old school" as in ???