The Society of St. Pius X has been hosting annual U.S. pilgrimages for nearly two decades. From their site:
Pascua Florida Pilgrimage to St. Augustine
March 29-April 3, 2016 6-day, 100 miles (75 miles of walking and 25
miles of canoeing) to St. Augustine, FL, the oldest
continuously-settled city in the United States. Discover more about
Cataldo Pilgrimage to Sacred Heart Mission
July 22-24, 2016 3-day, 50-mile to Sacred Heart Old Indian Mission
in Cataldo, ID, the oldest Catholic church in Northwest U.S., founded
by Fr. Pierre-Jean De Smet. Discover more about this
Santa Fe Pilgrimage to Padilla Cross
July 22-23, 2016 33-miles overnight (men and boys only) to the
monument at Lyons, KS, erected to honor America's Protomartyr, Fr. Juan
de Padilla (+1542). Discover more about this
There's also a Starkenburg Pilgrimage and an Auriesville, NY, pilgrimage, which honors "a group of Jesuit priests and religious [who] were martyred by the Iroquois Indians" "over 400 years ago".
The American branch of Tradition, Family, and Property (TFP), a lay Catholic group, also does Marian pilgrimages.