Ooh, ooh, ooh, this question was made for me! I've lived in all 3 places.

OK: Yale has some similar college town vibes in the Westville area to UM/Ann Arbor, but abundantly better food and a much more diverse scene in terms of food, people, languages spoken, etc. The hills in Connecticut are much better than Ann Arbor and Chicago, both. Still in temperate forests, so if you like the woods, you'll be happy there. Because of East Rock, West Rock, Sleeping Giant, etc., you can get some really nice VIEWS of the woods and the hills. You're only 3 miles (oops, no, EDIT: hours!) from the Greens and the Whites, which are some more serious hiking ranges.

You're also close to the ocean, which is very different than the midwest. There are kettle ponds, but not really big lakes like you have in Michigan and Illinois. Still, the sound is lovely, and there are some very accessible beaches within 20 min of NH.

Art culture is great in NHV. Chicago has a great museum and arts scene, as you're well aware. and NHV is a lot smaller, but does have some great museums and arts especially for its size. Also, <2 hours from NYC, so you can get a true metro fix pretty easily. And 3 hours from Boston.

IMO, NHV is superior to Ann Arbor on pretty much all fronts, but if you're a big city person, you might prefer Chicago. That being said, NHV is definitely a city (much moreso than A2, which felt pretty suburban to me) but much smaller.

PS - no offense if you love A2. Had a good time there, but it didn't really feel like a perfect fit for me.