Fallout 3/Picking up the Trail

NOTE: You can skip earlier quests if you can glitch or cheat your way into the Citadel. If you find your way in (either by toggling collision or by using a physics glitch to jump over the gate), all you need to do is access the terminal containing information about the various vaults. At that point, you can head to Lamplight Caverns.

This quest starts as soon as Dr. Li reaches the Citadel during the escort run through the Taft tunnels.

Power Armor training
Once you enter the citadel, you can obatin permission from Elder Lyons for Power Armor training. To receive it, speak with Paladin Gunny. He may be found in the live-fire training area during the day, when he's instructing the new recruits.

Pre-war computer access
Scribe Rothchild will give you access to pre-war computers to get information; he is located in the laboratory (and identified by the VATS compass); while he is unaware that a G.E.C.K may exist, he does direct you to the Vault-Tek computer located in the A-Ring; after checking the computer, you will find that Vault 87 has a G.E.C.K. in the non-standard equipment.

Return to Scribe Rothchild, and he will inform you of the location of Vault 87 by providing you with a map; this map also contains the locations of a few other vaults as well if you haven't seen them already.

If you want, you can proceed with some other side quests if you haven't otherwise determined the locations of the vaults:
 * Agatha's Song

Vault 87
Vault 87 is surrounded by a strong radiation field; as such you cannot safely approach the vault from the surface. It is not feasible to proceed through the field; even at the maximum of 85% radiation resistance, you will receive in excess of 500 rads/second near the vault entrance - in addition, the surface entrance is not usable.

There are a few radaway packs and an advanced radiation suit at the vault entrance, but it is not worth the amount of Radaway packs required to reach them.

The only way to reach the vault is by an underground entrance through Lamplight caverns.

Lamplight caverns
You can enter lamplight caverns using the speech skill or using the Child at Heart perk. If you are unsuccessful, you can obtain a quest from the mayor to rescue two kidnapped children from Paradise falls.

Through lamplight caverns, the mayor explains there are two routes available to Vault 87.
 * One is Murder Pass, which is infested with monsters and traps, but contains a few "rare" items.
 * The other is through the door and is available by speaking with Joseph combined with Science 50. This leads directly into the vault Reactor Chambers.

Entering Vault 87 starts the next portion of the main quest, Finding the Garden of Eden.