M.M.
Welcome to El Paso! I am in two moms groups - Mothers and More is a great group that offers playdates, park dates, moms nights out and more - it meets on the west side so if that is not convenient to you that group might not be good. I am also in a MOPS group and there are a handful in El Paso so there should be one close to you wherever you are in the city. Also the library has free story times which is a good place to socialize.
I hope this helps!
M. :)