Eric M.
Yelp
I was a member at the Union League Club for a few years and it does a lot of things well. The "Club" aspect and the "hospitality" aspects, it does as well as anywhere else in Chicago.
If you like the idea of a place you can go and just hang out in a quiet atmosphere (most of the time), if you like the idea of watching boxing the way it was meant to be watched (wearing formal wear, in a temporarily converted formal dining room, with all your best buddies and buckets of good beer), if you support the idea of the UNITED States of America, it's a stalwart in all those areas.
If you're a businessperson, or part of the professional class (banker, lawyer, doctor), it's a great place to make contacts, network and host professional events.
That said, the Union League Club isn't for everyone. Even if you make good money, have good pedigree, know how to mind your Ps and Qs, and like club atmospheres, there are reasons you may not want to join the Union League Club.
If you don't wear at least business casual clothes to your job, it will make it difficult to take full advantage of the cub due to dress codes. This applies to a lot (though not all) of technology professionals. Sure you could dress just for the Club, but do you really want to dress differently just to conform to their standards?
If your ideas are more progressive than mainstream compared to Chicago politics, it may not be a great fit. They won't look down on you or cause you problems, but you won't find them lining up to support causes you believe in, either. The Union League is very civic-minded, and if you're going to join a civic-minded club, it kinda makes sense to be able to agree with them often enough that you feel your efforts are helping and being helped.
If your ideas on society put an emphasis on open access and transparency above comfort and friendship, not just politically but as a way of setting up public life, you may not feel like it's a great fit. The premier example of this is the raw pride the Union League Club exhibits in the Harold Washington Library. Unlike most recent major public libraries, Harold Washington is about being an imposing citadel, defending the books from attack. The regular library is deep inside - you don't see books for a while after walking into the library. A more modern, humanistic library would make the information feel much more accessible.
All that said, the Union League Club is a great institution. It's not very modern, but it serves some good purposes for the city, state, and even nation. Check out the building during an open-to-the-public event (they host some occasionally), and if you fit the profile seriously consider joining up. If you don't fit the profile, there are other ways to make an impact in this city.