I vote the Shrine of the Most Blessed Sacrament. The Shrine is about 40 miles or so out of Birmingham. Up that way is also Casa Maria, where the Sister Servants are. They have very good weekend/day retreats there (just got back from one). If you can’t make the whole day and just want to come by for a couple conferences, the sisters are so kind and I am sure they would be fine with that. Then you can stop by Ave Maria Grotto as well. It is neat to see too. There is the Cathedral, which is beautiful. And you can make a stop by EWTN, attend Mass, see the studios, visit the gift shop, walk the grounds, and see a live show.
I haven’t been to Maria Stein yet. It looks very neat though. I hope to visit next Spring. It certainly would be a very special place to make a little pilgrimage too.
Another place is the National Shrine of Kateri Tekakwitha. Bob and Penny Lord did a video there before. You can visit the grounds where she lived much of her life. You can visit the chapel which commemorates the chapel where she was baptized. Her body is buried in Quebec though at Ste-Catherine de la Laprearie, another place to make a pilgrimage too to seek the intercession of the little blessed Indian girl.
katerishrine.com/index.htm
There is also the “Shrine” of the Venerable Solanus Casey in Detroit, Michigan. He has a wonderful story, and his body was found to be incorrupt, despite water filling the tomb. His tomb is at the shrine.
A friend of mine recently made a pilgrimage to the National Shrine of St. John Neumann. He had a very blessed experience there. the Saint’s body is there, displayed in a glass case. From what I understand it is a beautiful shrine to visit as well.
stjohnneumann.org/
Another American saint shrine is that of St. Katharine Drexel. I googled it and found an article describing the shrine:
nbccongress.org/lifestyle/saint_katharine_drexel_shrine_01.asp
Here is a good site to look for Shrines and Basilicas to visit in the U.S. and Canada:
catholicusa.com/basilicas_&shrines/basilicas&_shrines.htm