In Indy, everything is in proximity to one another. Hotels, bars, restaurants, the circle (very cool), other misc. eateries are all walking distance separation. It's a pretty incredible experience for those who haven't. There are carriage rides down close to the circle, you can tour the fabulous Lucas Oil Stadium and visit the Colts Pro Shop, and the list goes on. It will be back in 2020 and 2022 so that's a long time, don't miss this venue!!
While I agree that Indy is a great venue in terms of convenience for visitors, it still has its negatives.
One is that the city as a whole is relatively small and not a "hub" of Big Ten alumni. Yeah there's a lot of Purdue/IU alumni, but outside of that - no school really has much. This relies on travel for most fans, which can hamper attendance (which we've seen with poor attendance for championship games).
Secondly, while it's not necessarily a bad thing that fans have to travel, Indianapolis is just not a Chicago, New York, DC in terms of entertainment. Unless you're going to every session, there's limited things to do in Indianapolis (particularly if the weather is not great). There ARE things to do and improvements have been made, but the fact that you point out the Colts Pro Shop as a tourist destination....speaks to the issue. So people may go for one year. But will they want to return year after year - I mean once you go to the NCAA Museum, there's no need to ever go back. And quite frankly, while the restaurants have improved in Indy, some other retail has gone down - Circle Center is not a shopping destination whatsoever anymore. When your most "exclusive"/rare store is H&M, there's an issue.
Chicago, in my opinion, would be THE place to have it - but with one major caveat. The United Center blows. Not only in terms of venue, but also location. Chicago has a ton of Big Ten alumni (although maybe not as much Rutgers/Maryland) and is an easy place to travel, both convenient driving from most Big Ten schools, but obviously has major airports as well. It's also a very entertaining place to go.
I have mixed emotions on NY/DC. Personally, being in the DC area, it is great. DC is also easy to travel to and does have a lot of Big Ten alumni. However, long-distance alumni typically are not as well connected to the university. Am I going to buy an all-session pass? Probably not. And you also will see the same issue you see in Indianapolis. With there being a lot of travel involved, if you end up even with a Purdue/Michigan State final - I'd be surprised if attendance was higher than 10,000 (which the Verizon Center seats 21k). To me, that's not an attractive look. There isn't a "Big Ten" interest in DC where you're going to have a bunch of randoms going. And the Big Ten alumni in this area are not as well connected, so once their team is out, their interest is also probably out. But with DC, once Maryland is out (or not playing in the session) - I don't know how great attendance will be.
So DC and NYC are fine in terms of to have it there 1 year - it will be a destination spot for fans to travel to. NYC will obviously be weird with having Big East there too. But NYC and DC are also fan-friendly. You can stay in a hotel right by the arenas, you can walk/public transport everywhere, lots of things to do, etc.
Overall, I'd prefer to have the tournament in one location each year. However, there isn't one obvious answer and all locations have major pluses and minuses. I'd love Chicago, but do not care of the United Center. They're building a new arena at the convention center closer to downtown, but the problem is that it's only 10k seats, so no chance the Big Ten moves to that.