New Mexico

My understanding as someone who has been in New Mexico not quite a year and a half is that it has the oldest state capital and a bilingual constitution.[1] It is the oldest living culture in the US with still living Pueblo cultures going back a thousand years. It is highly multicultural with a mix of English, Spanish and Native American cultures and languages.

There's a lot of "normal American food" here. You will have zero problem finding familiar burger joints and pizza chains.

And then there's stuff I've never seen before which may or may not be peculiar to New Mexico. 

Piñon coffee

I can't find a Wikipedia page. If I search "pinon coffee," most of the top hits mention New Mexico or places in New Mexico, like Albuquerque, and my recollection is the first time I searched for it online, it said something like it's coffee of the American Southwest, especially New Mexico.

This is the Copilot answer:

Piñon coffee is a unique beverage made primarily from the seeds of the Colorado piñon tree, which are roasted and ground to create a rich and flavorful coffee. It is often blended with Arabica coffee beans and may include piñon nuts or a custom piñon flavoring to enhance its distinct smooth and nutty taste. This coffee is particularly popular in the southwestern United States, where it embodies the region's cultural heritage and is celebrated for its unique flavor profile and potential health benefits. 

I have yet to try it. I saw signs for someone selling piñon and initially misunderstood it to be someone advertising a birthday party or party service with piñatas. My initial online search brought up something else, maybe the tree, and I tried again because I was like "No, they weren't selling roasted firewood." (or whatever) and added the word "coffee" to my search term.

Navajo Tacos

I have yet to try this. As someone who has no idea WHAT I'm talking about, this is apparently a variation in tacos made with Native American frybread instead of taco shells. It's on the menu at a local chain that seems to be found only in New Mexico called Weck’s. From their website:

Since opening our doors in 1991, Weck’s has been more than a breakfast and lunch spot—it’s been a place where New Mexicans gather, connect, and start their day right.

Born in Albuquerque and grown from local roots, Weck’s was built on a simple belief: that great food and genuine service go hand in hand.

The decor reads like a country vibe catering to ranchers or something, only not exactly the same vibe you would see in Georgia where I grew up. The menu seems to be a fusion of "standard American food," Mexican and Native American.

I've only eaten there a few times and still haven't tried the Navajo Tacos. I have tried the posole, which is a spicy soup made with hominy and pork that I had never heard of before. 

There is a Wikipedia article on New Mexico Cuisine and my recollection is that someone on Reddit suggested that the landscape of Courage the Cowardly Dog, set in a farmhouse near a fictional town of Nowhere, Kansas, actually looks like rural New Mexico. As someone who has spent time in both states, it looks a lot more like New Mexico to me than Kansas. And there is an article exploring the question did New Mexico inspire the creation of this show.

I grew up in Columbus, Georgia which has a substantial German-American community. I was in my thirties when I learned there are grocery stores in the US that don't carry roulade meat and butchers who have no idea what that is or how to cut it. I had to go find a package of flank steak and explain how I wanted it cut.

I have no idea what New Mexicans would think is "New Mexico food." They probably think what they eat is normal, both the stuff I'm familiar with and the stuff I initially misread as piñata, and I'm the weirdo.

Footnote 

[1] Someone on Reddit said it's a bilingual state and has been from the beginning, with a bilingual constitution. A search for how many us states hsve have a bilingual constitution gets me:

Hawaii is the only U.S. state that has a bilingual constitution, officially recognizing both English and Hawaiian as its official languages. Additionally, Hawaii is the only state with two official languages, while California has a constitutional provision for Spanish. 

But a search for is the new mexico constitution bilingual gets me a resounding YES:

Yes

Yes, the New Mexico Constitution is bilingual, as it recognizes both English and Spanish as official languages. This bilingual status is reflected in various provisions, including educational rights and language access in public institutions. The Constitution was adopted in 1911, and it has been amended to ensure the rights of Spanish speakers and the preservation of the Treaty of Guadalupe Hidalgo. 

From the Wikipedia article on New Mexico:

Official language

New Mexico's original state constitution of 1911 required all laws be published in both English and Spanish for twenty years after ratification; this requirement was renewed in 1931 and 1943, with some sources stating the state was officially bilingual until 1953. Nonetheless, the current constitution does not declare any language "official". While Spanish was permitted in the legislature until 1935, all state officials are required to have a good knowledge of English; consequently, some analysts argue that New Mexico cannot be considered a bilingual state, since not all laws are published in both languages.

And the Wikipedia page for Constitution of New Mexico starts with:

The Constitution of the State of New Mexico (Spanish: Constitución del Estado de Nuevo México) ...