Negotiate with whatever remnants of Caesar's army might remain, as in: "You have 48 hours to get moving East before I give The Fort to the Boomers as a bombing range and encourage them to practice often."
Notfiy the Boomers to wait 48 hours, then
sterilize the Fort. Next, negotiate regular air patrols with an onboard (unarmed) Securitron for communication. Yes, I know, Goodsprings is too far for direct communication.
But- with a Securitron onboard, a pass near New Vegas can relay communication of sightings faster than landing at Nellis and sending a runner.
Negotiate with NCR: Under what conditions they will be allowed to trade with
my territory, and what taxes any of them who wish to stay in (or operate in) said territories will pay. Allow free passage for removal of their military from my lands on a "so long as none of your people start anything" basis. Any resistance or grumbling will be met with the question "Would you like the deal I offered what's left of the Legion? It
can be arranged..." Continued military presence open to negotiation, but not as "occupying force." Troops need R&R, Vegas New or Old is R&R.
Begin cleanup and renewal operations, setting up committees and local governments as appropriate- for instance, the Kings and Followers in Freeside. Kings working security patrol and cleanup, Followers on workforce coordination and medical. Interfere as necessary to initiate a workable balance, though I honestly don't see much necessity- The King seems to have the right basic idea already for the most part.
Sin City, right? Solve Fiend problem by alliance with Great Khans, Fiend cleanout sweep, Khans granted "recreational chemical" concessions for entire area. Begin "rehabilitation" of encouraging med production, coordinating with Followers.
Bring in more small businesses on the Strip, as has already been mentioned in other posts.
Make very harsh examples of senior Omertas and radical White Gloves, let their replacements know they are on a very short leash and being watched.
Initiate relations with Jacobstown. (Gourmand now serves best Bighorner Steak on the Strip, any Mutants willing to talk first rather than shoot offered directions to a nice welcoming home. Long-term goal, mutant-friendly Strip. Expanded, jointly-run Westside/Jacobstown co-op?)
Locate Tabitha, boost Black Mountain transmitter range- Best Friend Tabitha show = potential gold mine.