And away we go...
It looks like Virginia Tech's facility came in at about $400/SF (lots of guesses and assumptions). If the building 1) is a pre-engineered metal building with minimal architectural features, 2) has few if any break-off rooms, and 3) has a very simple HVAC requirements, then that is a low price even in a right-to-work state. It is possible that they subtracted out some donations and gifts which offset some of the costs or got a great deal from a contractor that was a fan.
For NU's proposed facility (just the open practice area and not including any of the ancillary spaces which will be more expensive on a square foot basis) I would add 8% for being in a union area rather than a right-to-work state (sorry union folks, this is a real number based on my first hand experience). I would add another 10% based on general higher prices in urban Chicago rather than rural Blacksburg (in the US, competition for labor surpasses materials costs, the materials would probably cost about the same since mark-up would be higher in Chicago against lower transportation costs), I would add 5% for the fancy window wall shown in the architects drawings, I would add 10% for HVAC requirements due to the window wall, I would add 5% for soft costs due to permitting, and I would add probably 50% for the foundations required due to depth of bedrock and wind speeds. Finally, I would add about 15% assuming that the window wall and other factors require a significantly different structure than a more standardized design. So we are looking at $812/SF for just the open area practice facility without taking into account any other niceties or finishes proposed for the NU facility. In reality, probably $900 - $1000 per square foot would be a reasonable guess which would make NU's open area practice facility well over double Virginia Tech's on its own.
The remainder of the ancillary interior and exterior spaces being far more expensive than the one large open area would be expected.
Of course, all of this is totally fabricated off of two numbers and my memory of some renderings of NU's facilities which I have not looked at in weeks. But hopefully it gives an idea of the kind of costs we may be looking at on the lakefront in Chicago versus Virginia Tech.
Yes, I am taking a kind of silly post seriously but it is June.