I'm a few hours south.
Honestly, as a big city girl, I think you would LOVE Chicago. Tons to do, the shopping OMG. If you like concerts and plays and all that stuff you really don't need to look anywhere else. Just about any artist you would ever want to see will play Chicago. One of the best concerts of my life took place in a small old theatre up in Chicago... it was amazing. And seriously, the shopping. Plus all the museums, the zoos, the aquarium, frickin' Navy Pier.
It would also be awesome for you because you really don't need a car. The public transport system will take you pretty much anywhere you want to go. Some of the lines are a bit janky and nasty but it IS Chicago, LOL. You can cab it if you want but there's really no need, plus that's expensive and the public transport is way cheap.
But as a Florida girl you might also hate it, because they do tend to get lots of cold lake effect weather. I will say, however, that Chicago is beautiful in the snow.
When it doesn't look like this.
KIDDING... I'm almost 28 and I can only think of twice in my life, counting last year, that we had snowstorms THAT bad. Chicago always gets more than we do down here but it's not like Lake Shore Drive gets buried in snow every other week in winter. It's really not super common. On the up side, a friend of mine who moved up to Chicago went SNOWBOARDING in the city when it snowed like that. Urban snowboarding. In Chicago. How cool is that?!
And yes... it's a Catholic private university... I think that is something you need to do a lot of soul searching on more than if you think Chicago is going to be too cold for you. Their website talks plenty about diversity and people from all kinds of faiths but it's still a Catholic university. I visited a Christian college years ago and they aren't going to be forcing people to go to church on Sunday and stuff but it's definitely still a Christian college and you can tell.
ETA: Linds lives in a suburb near Chicago. I think we have a few Chicago suburbanites on the forum actually. I have considered Schaumburg personally... it's a nice little place and THAT'S WHERE IKEA IS.
ETA2: The other nice thing about Chicago is you have an international airport there, so you can fly pretty much wherever you want right from there, or people can fly in there. So it will be great for your family. Though I think Boston also has an international airport, so that one isn't any different for you.
It really is a lovely city. I love to visit and play. Something about it just gives me a major thrill and puts "Sweet Home Chicago" in my head, even though I've never lived there or called it home LOL.
I don't know if I could truly live there a LONG time, but I could do a year or two pretty easily before I started wanting some acreage LOL.