They Went That-a-Way

 is a quest in Fallout: New Vegas. It is also an Achievement on the Xbox 360 and PC; and a Silver Trophy on the PlayStation 3.

Objectives

 * Find the man who tried to kill you.

Overview
You're ready to mosey on out of Goodsprings and find that guy in the checkered suit. Get looking! If you already killed Benny, you don't have to complete this quest.

Primm

 * Go to Primm, a bit south-east down the road from Goodsprings Source.
 * When you arrive, you'll be stopped by an NCR trooper, who tells you Primm is off limits, and to stay on the west side of the overpass if you don't want to get shot. The east side of Primm (the side where you can see the roller coaster) has been overtaken by Convicts.  Note that although they may be referred to as Powder Gangers by NCR officials, killing them does not affect your relationship with the Powder Gangers as these convicts are separate from that faction.
 * If you ask the NCR for help, they'll just say it's not under their jurisdiction, and even if it was, they're desperately low on supplies and extra hands.
 * Go into Primm and kill everyone who is outside (eight convicts - 5 around Vikki and Vance Casino and 3 on the tracks of broken roller coaster).
 * Enter Vikki and Vance Casino and talk to Johnson Nash about finding the man that shot you.
 * Note that the companion ED-E can be located in the courier office which is Johnson Nash's home. To repair ED-E you must pass a repair skill level or have sufficient parts.  Activating ED-E opens the quest ED-E My Love.

Nipton

 * Skipping past My Kind of Town, head to Nipton (down the road south, then east).
 * You'll find only two people, the rest have been killed, tortured and crucified by Caesar's Legion.
 * Go into the store on the left to find the second survivor, Boxcars, who tells you that they took a few hostages, and that you need to go to Novac. Speaking to him about this opens up the quest Booted.  You can also gain Karma by giving Boxcars Med-X.
 * Lastly, Vulpes Inculta addresses you if you approach the town hall. He is a Frumentarii, a high-ranking Legion agent. He will tell you of what they did so you can spread the word, which gives you the mission Cold Cold Heart.

Novac

 * At Novac, ask around and find Manny Vargas (located in the T-Rex during the daytime).
 * Go through the Dino-Bite Gift Shop and talk to Manny:
 * He will make you clear out a building to the west, the REPCONN Test Site, before he tells you anything, beginning Come Fly With Me. Players with the Confirmed Bachelor perk can skip this step.
 * You can also use the terminal in his hotel room to read his journal logs to trigger the continuation of the quest. No karma loss, and Manny will not turn hostile toward you, even if he witnesses you using the terminal.
 * Or you can just kill him and loot necessary quest item.
 * Or you can just steal holotape from his pocket.
 * You can also speak to Manny Vargas about his co-worker, Boone. Speaking to Boone can open up the quest One for My Baby, making him available as a companion.

Boulder City

 * Manny will then tell you that they went to Boulder City.
 * Go there and begin the quest Boulder City Showdown. About halfway through, when you talk to Jessup, you will complete.
 * Jessup will give you a quest item, Benny's Engraved cigarette lighter.
 * If you can end the showdown peacefully you can gain good karma with the Great Khans.

Behind the Scenes

 * The name of this quest is most likely the taken from the song Gun Street Girl by Tom Waits. Or, more likely, a looney tunes reference.