I feel like a lot of people on here live in NYC, and are therefore biased towards it. So as someone who used to live in Chicago, I feel like I need to give Chicago some love.
First and foremost, its impossible to avoid generalizations when you're dealing with cities full of 2.5+ million people. That being said, Chicago has way less people, so even though it is crowded and packed (big city vibes), it nevertheless rarely feels congested (except the freeways). Chicago is in the midwest, which means despite being a large urban area, it avoids a lot of the pretension and networking that LA and NYC possess. I found it was a lot easier to make genuine connections without feeling like people were constantly weighing you for coolness and clout potential. Chicago is cheaper, and despite being in the midwest, being right by lake Michigan makes it feel like you're on a coast. It was a great transition to the midwest from the west coast for me, slowly weaning me from my reliance on the ocean. Also the coastline where lake michigan meets the city is beautiful, and its a lot of fun to be able to swim off of the boardwalk right at the foot of skyscrapers. Chicago is also home of the skyscraper, and lets be honest, its a major city, and once you get up past 2 million people, you're going to be able to find all the culture and diversity you want (just at less of a premium and with less washed-up/trust fund artists that rely on the distortion of the hype machine). Oh, and Chicago has great food, parks, public transit, etc.
Anyway, I love Chicago. I feel like its often overlooked (vs. NYC and LA) which makes it the best option. In my opinion, both of those other cities are overplayed and overpriced. However, the good news is, with both of these cities as your options, you can't really go wrong.