They Went That-a-Way

 is a quest in Fallout: New Vegas.

Quick walkthrough
Well, now you're ready to mosey on out of Goodsprings and find that guy in the bad checkered suit. Get looking!

Detailed walkthrough
1. This is the overall objective in the quest. So don't worry about it. Finish the other objectives.

2. Go to Primm, a bit south-east down the road from Goodsprings Source. When you get there, you'll be stopped by an NCR soldier who tells you that 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 powder gangers. If you ask the NCR for help, they will just tell you that 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. There are about six powder gangers. If you go into the casino on the west side of the city you can find some NCR troops. Around here you will also find the quest

3. Skipping past My Kind of Town, Head to Nipton, which is down the road south, then east. Once there you find only two people. The rest had been killed,tortured and crucified by Caesars Legion. If you go into the store on the left you find the second, named Boxcars who tells you that they took a few hostages. You also figure out that you need to go to Novac.

4. The road to Novac is pretty easy. A few foes but nothing you can't handle. Once at Novac, ask around and someone will direct you to Manny Vargas. As in the guy in the T-rex.

5. Go through the T-rex gift shop and talk to Manny. Unless you have the Confirmed Bachelor perk, he will make you clear out a building to the west before he tells you anything. This will lead you to the Come Fly With Me quest. You can also use the terminal in his hotel room (No hacking required, also no karma loss, and Manny will not turn hostile toward you even if he witnesses you using the terminal) and read his journal logs. This triggers the continuation of the quest also. (If you clear out the building to the west before going to Manny, the mission may not trigger "complete" even if you go back over to the already-cleared building.)

6. After you do that, he will tell you that they went to Boulder City. Go there and do Boulder City Showdown About halfway through you will complete They Went That-a-Way.