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 repaired, every now and then, ED-E will begin playing a recording made by the Enclave researcher. This is possibly triggered by certain keywords in NPC speech, or at random intervals. Eventually, a Brotherhood of Steel patrol Knight, Knight Lorenzo, will contact you through ED-E, interested in examining ED-E. The Knight asks you to take him to a Brotherhood of Steel patrol inside the REPCONN Headquarters.

Using the "wait" feature will also speed up ED-E's speech events. Use the wait feature in increments of 1 hour inside Old Lady Gibson's house and after that anywhere else in the world.

Bugs
If you talk to Old Lady Gibson and go through all the dialog before you have ED-E, it seems you cant complete the quest. The needed dialogue options are no longer there. (XBOX360, PS3 and PC(fixcode: setstage 001572e8 10))

The bug can be bypassed by using the "wait" feature inside her house.

Talking about Archimedes II without having ED-E seems to cause problems too, going back after getting him doesn't trigger anything.

If you encounter Old Lady Gibson at Helios One and are forced to kill her for hostility, then the quest marker will lead you to her dead body, but nothing can be done. The quest just stays on your Pip-Boy and can not be failed.