This small Catholic church in Golden, New Mexico was built in the 1830s to honor St. Francis of Assisi while the town was growing from a gold strike. The latest restoration effort is detailed in this linked article from the Albuquerque Journal.
St. Anthony’s Catholic Church is in the middle of the village of Cordova and was built in 1832. The town is known for wood carving and is found off of the High Road to Taos route.
El Santuario de Chimayo is an important pilgrimage church located in the hills of Northern New Mexico. Initially a Catholic chapel was built on the site to serve the Spanish Mission, but was replaced by the current church in 1816. During Holy Week each year, about 30,000 faithful make the trip for a pilgrimage.
Walking the grounds, there are several small shrines and fences where visitors have left crosses. There’s also a room (El Pocito) in the rear of the church where dark soil from the area is blessed and taken by visitors for hopes of healing or cures. Although the room is filled with crutches and wheelchairs from visitors deciding they no longer needed them, the church hasn’t officially opined on whether any miracles have occurred as a result.
The Church has a website with a lot more information on the history and some of the specifics of the location – Sanctuary of Chimayo.
In the Sangre de Cristo (Blood of Christ) Mountains in northern New Mexico is a series of small pueblos. In many of them there is a small church established during the Spanish missions of the 17th century. This church in Picuris Pueblo (San Lorenzo) has changed over the years, and using historical records, it was rebuilt in the 1960s to resemble the church as it looked in 1778.