BC typically participates in an early-season tournament to get its feet wet and gear up for the season. Pre-season tournaments allow schools like BC to put a few easy wins under their belts while allowing lesser schools to test their prowess against top-level competition. As excited as I am about the Charleston Classic (not very), I think it would be way more fun to have an old-school, CYO-style Catholic tournament.
There are plenty of Catholic basketball programs to make this idea happen. For example, Xavier, Marquette, Georgetown, Boston College, Holy Cross, St. Joseph's, Sienna, St. John's, Notre Dame, Villanova, St. Mary's, Gonzaga, Dayton, St. Louis, Seton Hall, and Fairfield would be a pretty sweet lineup. The biggest problem with this group of teams is that it's Big East heavy, and you really don't want schools from the same conference lining up against each other that early in the season. But if you structured the bracket like this, you could minimize the potential in-conference match-ups.
How much fun would this tournament be? Book a great venue, like MSG, find a name for the trophy (the Archbishop Fulton Sheen Cup?) and fight it out for three days. Every team is guaranteed three games, with no more than one in-conference match-up. If the in-conference matchups become a sticking point with the Big East schools, you could drop two of them and use Creighton and Detroit as replacements schools.
There's nothing like a little Catholic school rivalry.