To obtain the next location, either threaten the deputy with a Speech skill of at least 40 or obtain Deputy Beagle's journal.
There are three ways to obtain Deputy Beagle's journal.
Free Deputy Beagle. After this, he can be convinced to help clear out the rest of the hotel with a Speech skill of at least 25. If he is spoken to before exiting the hotel and the Courier offers to give him a gun, his inventory will be opened. There his journal can be taken. Note that this is the only way to obtain the journal without accruing negative Karma.
Kill Deputy Beagle and loot the journal off his corpse.
Pickpocket the journal from Deputy Beagle. Doing this at any time will cause negative Karma.
After obtaining and reading the journal, or if Deputy Beagle has told the Courier the next location, the next stage of the quest will begin: heading to Novac through Nipton.
Head to Nipton (down the road south, then east). Upon arrival, the Courier will be approached by Oliver Swanick, who will claim to have won a 'lottery' there. The player may choose to continue on to Novac, skipping the remaining optional encounters, or investigate Nipton further.
Entering the store on the left, the Courier will find Boxcars, who tells them that the Legion took a few hostages, and that they need to go to Novac. Speaking to him about this opens up the quest Booted. One can also gain Karma by giving Boxcars Med-X.
Lastly, Vulpes Inculta addresses the Courier if they approach the town hall. He will tell them to spread word of what the Legion has done, giving the mission Cold, Cold Heart. An important thing to note is that if Boone has been brought as a companion from Novac prior to visiting Nipton, he will start attacking the Legion regardless, rendering Vulpes hostile and unable to be talked to.
(Note: Caesar's Legion Fame can be gained when speaking to Vulpes Inculta about the events that happened at Nipton. Proceed through the dialogue asking what happened until given the dialogue to agree with the method that Vulpes used. Upon agreeing the Caesar's Legion fame will be achieved.)
On the way to Novac, the Courier will be ambushed by several Viper gunslingers if they travel by the road up the hill. There are 4 - 5 on the ground with 2 above on the rocks, and at least one grenade rifle.
He will make the Courier clear out a building to the west, the REPCONN test site, before he tells them anything, beginning Come Fly With Me. However, if one wants to skip REPCONN, just go to Manny Vargas's motel room and activate the terminal there, a file called "Message: Khan hospitality" will be present; it says that the attackers are headed to Boulder City.
Manny can be killed, and the necessary quest item will be on his corpse.
The holotape can also be pickpocketed. Either looting or stealing the holotape bypasses Come Fly With Me.
With the Confirmed Bachelor perk, the Courier can tell Manny that he sees he's been neglected. Manny decides that the Courier's a nice guy, and will say where the Khans are heading.