Send Boone, Cass and/or Veronica off to the lucky 38 and stock the fridges. They'll clean them out in short order. Leave some food on ED-E, Rex and Lily to start some fights in your suite.

Wait, what? I got tons of stuff in my fridges, one fridge contains only Nuka-Cola (all types) and Sarsaparilla, will they drink those?
Anyway, I started in the house in Goodsprings that is directly across from the entrance to the saloon. I found out later that it is Easy Pete's house, he doesn't seem to mind me using his footlocker, wardrobe, and bed. He prefers to sleep on the couch it seems.
Next was the room at NoVac and finally the Lucky 38, right now I'm in the process of going back to NoVac and Goodsprings so I can mail all my gear to the New Vegas strip. Finally have enough ammo to use my pre-order grenade rifle.
However, if I discover items missing from my fridge I may have to transfer those items to the presidential suite in the Tops.
-JJ