Thanks to Go Dairy Free viewer, Janet, for emailing this restaurant as a recommendation. She went to the Benihana in Anaheim, California:
I just went there with a family that has Celiac’s disease. They did the whole meal non-dairy and non-gluten in front of us. No trouble at all, and a lovely show for everyone.
Since the grills are used to cook other foods containing soy sauce (wheat) be sure that it is a safe surface at your local Benihana where Celiac or severe food allergies is a concern. They do not typically cook dairy products on the grill, but some sauces may contain small amounts. Check with the restaurant.
Benihana has locations throughout the U.S. See their website for locations, menus, hours, etc.