Currently, the best fit for all of our programs is the ACC. We can be competitive in football and have a shot at the BCS, whereas we'd be grossly overmatched in the B1G. At the same token, both of our basketball programs would continue to flourish in undoubtedly the best conference in the nation, whereas we'd be thrust into a very mediocre B1G basketball conference that would be a distant second or third behind the ACC, and also would likely decrease the amount of TV exposure due to the amount of ACC bball games ESPN will televise. We'd be joining five or six other current/recent Big East members, so the connections and rivalries would be there and we wouldn't be an outsider, as we would in the B1G. Travel would also be far easier for our fans.
I don't understand the "grossly overmatched" part. while the Big Ten has more historic names, if you look at computer rankings over the past five years there is not a huge difference between the Big Ten and the ACC (or, frankly, between either of them and the current Big East).
Both would be miles and miles better than some Big East remnants/Big 12 rejects/C-USA clowns hybrid mess that would be another ticking time bomb.