ED-E My Love

 is a quest in Fallout: New Vegas.

Quick walkthrough
After talking to Johnson Nash about ED-E, this quest will be given to the Courier. After heading to the Gibson scrap yard once ED-E is a companion, ED-E will begin playing a recording made by Whitley, an Enclave researcher at Adams Air Force Base. He is sending ED-E, a special prototype for a combat Eyebot, to Navarro for further upgrades.

Detailed walkthrough
Get ED-E in Primm in the shop on the right hand side after walking into Primm from the broken bridge and moving straight ahead until you see a dead courier, the courier is propped up against the shop.

To fix the robot you need either a high science, a high repair, or you can fix it with spare parts (you need 1 Scrap Electronics, 3 Scrap Metals, and 2 Sensor modules).

Once he's repaired, head to Gibson Scrap Yard and talk to Old Lady Gibson. Follow through all dialogue with Old Lady Gibson and it triggers a response from ED-E.

Another response is triggered by talking to the Follower of the Apocalypse in HELIOS One about ARCHIMEDES II.

Another response is triggered after talking to Doctor Hildern at Camp McCarran.

After you've gone through and triggered these responses Knight Lorenzo from the enclave will contact you through ED-E interested in examining ED-E and asks you to take him to a Brotherhood of Steel patrol site.