I have been to both of these shops and you will find them both lovely.
Ooltewah is the cutest little town and the Chattanooga Quilt shop is sweet, but not huge. A few weeks ago they had some FQ's on sale for $1 each! And a nice selection of neutrals (which I always seem to need...). Margo and I met up there, and had lunch at the Tea Room nearby... wonderful!
So Bee It is a larger shop and full of fabric and yarn. It's in Ringgold GA, a few miles from the TN border. As Margo said, it is newly rebuilt after a tornado destroyed it.
You'll enjoy visiting them both! And don't forget the TN Aquarium in Chattanooga is awesome, as are some of the other natural sights such Ruby Falls, Lookout Mountain, and Rock City. Lots to see and do in and near Chattanooga!