I followed the Gophers to Charlotte in 2005. They lost to Iowa State in the first round. Both North Carolina and Duke were on hand, so it made for sellout crowds and a pretty good atmosphere even though they didn't play each other. The games were at the recently demolished Charlotte Coliseum which held around 23,000, but was pretty basic on the amenities side which is partly why it was replaced. This was the first NCAA bid since the academic scandal, so people were pretty fired up. Gopher fans by no means took over the building, but enough traveled to create an atmosphere at the game and the pep rally/Sota Social at a local bar the night before. If you're considering going, it'll be a fun experience.
If you plan to follow the Gophers this year and will buy tickets through the U of M after the site and dates are revealed, here's something from 2005 to keep in mind, assuming the same ticketing policies exist in 2013. We picked up our tickets after arriving in Charlotte. It turned out the tickets were for the Gophers' first round afternoon session only. The evening session first round tickets weren't included and neither was the second round, the latter only being distributed had the Gophers advanced. Unless we missed it somehow, this wasn't made clear by the U of M from the start. We just went to the box office at the Coliseum and bought tickets there for the remaining sessions. Luckily they had enough of a selection due to the large capacity and many locals holding off until the Tar Heels in particular were assigned there. However, that may not be the case at a smaller arena with a popular team or two on hand. So beware.