I know it opened in SC and Georgia. Best information I could find was that it opened in only 1,161 theaters, which is less than half the number of theaters most movies are shown in. I also saw it did open in one theater in Manhattan. That is all academic anyway now as it has been released to DVD.
My wife and I went to see Courageous here in Texas on the big screen at the Silverado theater at Bandera RD and 1604. It only played one or two days and we made sure we had tickets. Turn out was sparse as no one had heard of this movie outside the Christian community at that time.