"Are you certain? In my experience, there really isn't an "affordable medium size city" in the US."
Minneapolis.
A very, very rich urban environment (there are two cities there, after all) and cultural scene. Is currently, very affordable - even in the most desirable neighborhoods.
I don't consider Minneapolis much of a city - more like a giant suburb with some nice bike paths. I grew up on the Northside. Same for the few times visiting Denver. You're gonna be driving if you want to have a social life.
You simply cannot compare it to a similar sized European city, or to any of the "big city" style US cities on the East coast.
For this exact reason I split my time between Minneapolis and Chicago and plan to move to Chicago as soon as possible full time. The lifestyles are not remotely comparable.
Minneapolis is exactly what I was thinking of when I said, "there are affordable suburbs that technically lie within the cities legal boundary lines" and are therefore called 'city' but are actually suburbs. Lyndale, Cocoran, Harrison, and many other examples, are actually suburban but they are technically within the legal/tax boundaries of Minneapolis and get called 'urban', when they are not.
Minneapolis is a cool place, this is not an slight to the city or it's residents in any way. But Minneapolis is almost entirely suburban, and the parts of Minneapolis / St Paul that are actually urban (where "urban" means more than 75% of the buildings are 4+ stories), those parts are not affordable to families.
I would have argued that you're making a "no true Scotsman" argument until I remembered something. I used to have a house in a great neighborhood in southwest Minneapolis. I had a girlfriend who came to my house frequently for almost a year before she realized I actually lived within the Minneapolis city limits, and not in a suburb.
Honestly, I think it's a shame to limit the definition of "city" so stringently. Why can't a quiet neighborhood with tree-lined streets and kids playing outside be considered a part of the city and not a "suburb within a city?"
But whatever, I still think of it as the best city I've ever lived in and although I still work here, I miss living in it sometimes.
Minneapolis.
A very, very rich urban environment (there are two cities there, after all) and cultural scene. Is currently, very affordable - even in the most desirable neighborhoods.
Denver also fit this bill up until 3-4 years ago.