I had my first and second MG's while I lived in Chicago. When I bought them, I had off street parking, but that ended a year later. I graduated from college and moved to a different apartment in the Lincoln Park area and only had the GT at that time.
Overall, it was honestly a little demoralizing. I drove a lot and used the car to get out of the city with trips to Madison and Milwaukee and other places in Illinois and Missouri, which was fun.
The bad side was vandalism (my car was egged, parts like the antannae were broken off, and my BL tags on the sides were stolen), I was hit by a drunk driver without insurance overnight while the car was parked. Then I got rear ended by someone who basically took off after damaging the rear end. Later I was rear ended again at a stop sign and that driver actually had insurance, so that wreck repaired the other two. Oftentimes, I ended up parking several blocks from my apartment, which is not the greatest feeling in the world.
It was really too bad, the GT was so solid when I bought it but over the five years it was a DD it declined and I felt guilty about it honestly. Unless you have at least off street parking and preferably a garage, I would not recommend urban classic car DD ownership. Living in an apartment poses other problems for chemical and tool storage. Working on a car outside in the winter is also no fun. Paying for a mechanic to work on a more run of the mill DD classic can outrun the value of the car in the first place, too.
I still live within a major city limits, but its nothing compared to Chicago and frankly feels like a suburb. I also have a garage and vandalism is not a problem.
I forgot to answer the question. I see a lot of classics when I'm in LA (of course) and in Chicago there are always several LBC's and older BMW's and 911's. I was most recently in DC and didn't see a single one. I did see a Boxster run a red light and almost get creamed by a Suburban, though. Yikes.