Northeast and Mid-Atlantic. Washington has the National Shrine, the largest Catholic church in North America, open every day with daily Mass and confessions, and the Saint John Paul II National Shrine nearby. Maryland has the Seton Shrine, with the tomb of the first American-born saint, and the Grotto of Lourdes at Emmitsburg; Pennsylvania, the St. John Neumann shrine in Philadelphia and the National Centre for Padre Pio in Barto; Massachusetts, the National Shrine of The Divine Mercy in Stockbridge; New York, Our Lady of Martyrs at Auriesville, open from mid-April to October 19.
Southeast and Midwest. Florida has La Leche, on the ground where a Mass of thanksgiving was offered on September 8, 1565, Mary Queen of the Universe in Orlando and the Ermita de la Caridad in Miami; Louisiana, St. Louis Cathedral in New Orleans; Alabama, the Shrine of the Most Blessed Sacrament in Hanceville. Champion, about 15 miles northeast of Green Bay, was approved on December 8, 2010; Wisconsin also has Holy Hill and Our Lady of Guadalupe in La Crosse. Ohio has Our Lady of Consolation in Carey, the Sorrowful Mother Shrine in Bellevue and the Maria Stein Shrine of the Holy Relics; Indiana, the Basilica of the Sacred Heart at Notre Dame; Illinois, Our Lady of the Snows in Belleville; Michigan, the Solanus Casey Center in Detroit.
South and West. Texas has Our Lady of San Juan del Valle and the San Antonio missions; New Mexico, El Santuario de Chimayó; Colorado, the Mother Cabrini Shrine in Golden; Oregon, The Grotto in Portland. The California missions, founded by Franciscans from 1769, include Mission San Carlos Borromeo in Carmel, with the tomb of St. Junípero Serra, and Franciscan pilgrims also seek out the replicas of the Portiuncula chapel in San Francisco and at Franciscan University of Steubenville.
Good to know before you go: these shrines keep very different calendars. Some are open every day of the year and others only in season, so read each shrine's own schedule in the week you travel.