A life-sized (or nearly so) statue of her is in a gallery of American saints and beati in the National Basilica in Washington, DC. I'd expect nothing less from a national basilica since she was born in upstate New York.
There's a statue of her at the Basilica of Sainte Anne de Beaupre in Quebec. This too is appropriate since Kateri died not far from Montreal and is claimed as the first Native Canadian to be canonized as well as the first Native American. As an aside, it is nice that Americans and Canadians have celebrated their union through Saint Kateri, both lobbying for her canonization, rather than quarreling over who gets to claim her.
The Basilica of Saint Francis of Assisi in Santa Fe, New Mexico, has a lovely statue of her. She probably did not wear turquoise, but than again, Jesus probably had a Jew-fro. (Is that okay to say? Sometimes I go too far.) The statue doesn't reflect the fact that she was scarred from a bout of smallpox that killed her parents and brother, but that artist probably preferred to reflect her inner beauty.
If one were making the long haul (by East Coast standards) across the New York Thruway and wanted to stop for a quick pilgrimage, the town on Fonda is a good choice. The Franciscan Friars have a shrine to her there, not far from the village where she lived. Visitors will find a chapel for Mass, a museum with artifacts from the area, a reconstructed village, and of course a gift shop.
About four miles down Route 5S in Auriesville, pilgrims will find the Shrine of Our Lady of Martyrs, which honors not only Saint Kateri, but Saint Isaac Jogues, Saint Rene Goupil, and Saint John LaLande. [They are collectively entered into the canon (and hagiomajor) as the North American Martyrs.] This shrine is operated by the Jesuits. With all due respect to the Franciscans, the Auriesville shrine looks even more appealing than the Fonda shrine.
I wonder if there was grumbling when she was added to the martyrs down the road. Saints Isaac, Rene, and John were all tomahawked; Saint Kateri died of her frail health. It feels like poaching to me, perhaps not in honoring her on the grounds, but certainly in featuring her so prominently on the shrine's website. I will be crossing the Thruway soon, but not soon enough to visit both sites. While the Jesuit site is already open for the season, the Franciscans won't be welcoming pilgrims until the Feast of Jeremiah the Prophet. It's probably for the best, since I doubt I could resist an attempt to get the Friars to dish on their blackrobed brothers down the road.