Fallout: New Vegas/They Went That-A-Way

Having finished the tutorial, you must now search for the men who tried to kill you.

Primm
Head to Primm, which is southeast of Goodsprings. Upon arriving, an NCR trooper will tell you that Primm has been overrun by convicts. Ignore his warning and enter the town. There are approximately six convicts, and you must kill them all to liberate the town. Once you do so, enter the Vikki and Vance casino and talk to Johnson Nash. He'll tell you to head to Nipton.

If desired, you can examine other conversation options to obtain the ../My Kind of Town/ quest, where you need to rescue deputy beagle inside the nearby hotel.

Nipton
Follow the road south of Primm and then go east. Upon arrival, you'll find that everything's been burned to the ground. You'll find a group of Legion soldiers led by a man named Vulpes Inculta, who will tell you to spread word of what you've seen. You can then find a man named Boxcars inside a store, who will tell you to go to Novac.

Novac
Follow the highway out of Nipton and head north to find Novac. Once there, you have several options of how to proceed.
 * 1) Talk to Manny Vargas (located in the T-rex mouth during the daytime) and complete the quest Come Fly With Me to get him to help you.
 * 2) Talk to Manny Vargas and use the Confirmed Bachelor perk to get him to tell you where to go.
 * 3) Read Manny's journal logs on his terminal in his hotel room to find out where to go.

Boulder City
Take the road north out of Novac and make your way to Boulder City. Once there, talk to Lieutenant Monroe to start the quest Boulder City Showdown. Complete this quest to complete "They Went That-A-Way" as well.