What I was thinking of is a cuisine where the name of the cuisine includes a state (or Region) and the name itself is well known. Something that woulds work for ,say, a one line description of a restaurant in a guidebook.
House of Edibles, 123 Main St--German (or French, Italian, Scandinavian, Chinese, California, Tex Mex...)
I don't see "New Mexico" being well known enough that most readers (even American readers) would know what kind of foods a restaurant would offer, in the same way they probably would know Tex Mex.
No, you don't notice a distinct cuisine in California. "California cuisine" is not the same thing as "cuisine of California." California cuisine is a distinct style of preparing and serving food, just as French cuisine or Chinese cuisine are. Wikipedia says:
California cuisine is a style of cuisine marked by an interest in fusion cuisine (integrating disparate cooking styles and ingredients) and in the use of freshly prepared local ingredients. The food is typically prepared with strong attention to presentation. The term California cuisine arose as a result of culinary movements in the last decades and should not be confused with the traditional foods of California.
Alice Waters, the proprietor of Chez Panisse restaurant in Berkeley, California, has contributed significantly to the concept of California Cuisine.