Courthouses in Eunice, New Mexico, the US. Courthouses locations in Eunice, New Mexico. Find the nearest courthouses locations, near you. All types of business services ATM Bank Courthouse Finance School All courthouses in Eunice Eunice Municipal Judge Courthouse +1 575-394-2635 1323 Main Street, Eunice, New Mexico 88231 Write a review Phone Directions Lea County Magistrate Courthouse +1 575-394-3368 2200 Avenue O, Eunice, New Mexico 88231 Write a review Phone Directions