You will have a nice collectable car here. It will attract a lot of attention as it could be worth something in the collector marketplace, so you will need a secure place to park it.
As a daly driver, it would be a shame if it got any dents or scratches in it from that Chicago traffic. Basic liability insurance should not be a problem, but you would need a special policy to cover collision damage. Also if someone hit you, even if they have insurance, determining the value of your vehicle could be difficult.
It will need a tune up about every 12,000 miles, thats plugs, points and condenser. You find it difficult to find a mechanic that can install and set the points. This could be something you could learn to do yourself, the tools required aren't that much.
You can go 5,000 miles on a modern 10w30 oil but a 15w40 diesel oil would be better.
Brakes are going to be a problem. The drum brakes from the 60's and earlier worked just fine. I would actually put them up against anything today for first stop performance. They tend to fade after multiple hard stops like in racing.
However, in the 60's, the shoes were lined with asbestos. Today, you cannot get those linings. Now, while disk brake pads have some high performance materials available, there doesn't seem to be anything like that for drum brake shoes. Consequentially, the brakes will not work as good today as they did when the vehicle was new. In Chicago, you will need good brakes. Having said all this, I think that Buick did offer disk brakes on front as an option that year so you may have them.