There is no U.S. Consulate in El Paso. The consulate that processes immigrant visa packets for Mexican Citizens in Mexico is Ciudad Juarez, Mexico. If you were 'admitted' into the U.S. at El Paso, then your permanent resident card may indicate that place of admission as El Paso.
Use the place of admission. If you were admitted in an airport, then use the airport city. If you filed for adjustment of status, then use the U.S. City where you had your I-485 interview.
Yes, you could conceivably use the City where you lived at the time you applied for adjustment or admission into the U.S. The USCIS will cross check and approve, where all the other questions tend to confirm your identity.
When applying for a green card replacement, you can be asked for certified copies of all your criminal records, if any. There may be other questions asked that may get you into trouble. If you were ever arrested and/or convicted, then consider scheduling an appointment with an experienced immigration attorney.
The above is general information and does not create an attorney client relationship.