Elizabethtown is an unincorporated community in Colfax County, New Mexico, United States. It is located just off New Mexico State Road 38, between the communities of Eagle Nest and Red River. Elizabethtown is situated just east of the Carson National Forest. The community is a former mining town and lies northeast of Scully Mountain and west o…Elizabethtown is an unincorporated community in Colfax County, New Mexico, United States. It is located just off New Mexico State Road 38, between the communities of Eagle Nest and Red River. Elizabethtown is situated just east of the Carson National Forest. The community is a former mining town and lies northeast of Scully Mountain and west of Baldy Mountain.