Now that all of the major conference tournaments are televised, I am not really sure whether it matters anymore where they are played. As a fan, I am not going to tune into the Big East tournament because it is being played at MSG. Similarly, my (lack of) interest in the Atlantic 10 tourney has not changed since it went from Brooklyn to Pittsburgh. Being near a media hub was important in the '80s when there were limited media outlets and being close to them could mean additional coverage. Now, there are so many avenues to read, watch, learn about your favorite team, I do not think it matters.
In reality, there are only two issues that are important when choosing where to play a conference tournament: recruiting, and to a much lesser extent, fan experience.
The problem with number one is that it can be regional. Is playing in NYC (MSG or Barclay) matter to someone outside of the northeast? How much time do the kids get to enjoy what a larger city has to offer (this is not a rhetorical question, I do not know)? I would guess very little and the players mostly see a hotel room, bus and the stadium. How much harder and more expensive is it for a non-NE player's family and friends to come to the games? I think playing in an NBA arena is a plus, but unless you grow up a fan of the team or a player on the team, does it matter which NBA Arena to a 17 year trying to decide were to go to college? For Syracuse, it probably benefits recruiting playing in NYC or D.C. as the locations are near our traditional recruiting areas. For Clemson or Wake Forest, probably does little or nothing to assist in recruiting, but playing in North Carolina might.
The second issue is fan experience. There is no question that a large city has more to offer fans than a smaller one. I would much rather spend an extended weekend in NYC than in Greensboro. Again, however, this can be regional. Living in the Midwest, regardless of where the tournament is located, I would have to fly and would be stuck in the city/area of the tournament even if my team was a one and done. This would not be true of fans living near the tournament site. This could be a detriment to attendance of having the tournament further away, as would potentially having fans wanting to travel the next weekend as well for the NCAA games. The reason the Big East games at MSG were great was because so many school fanbases were able to pack the arena, the same reason ACC lifers probably fondly reflect on Greensboro. The size and geographic area of modern conferences no longer make this possible. Case in point, the only people I have heard positively discuss the location of the B1G tournament this year (DC) and next (MSG) are those that live nearby.
If it were up to me, I would have all of the conference tournaments played at casinos in Las Vegas. I could see both of my alma maters play and if they both were one and dones, I would plenty to do, including checking out other conference tourney games