just like fallout 3, i imagine you can make any place you want your home
Having just started playing, I found a couple of beds I could sleep in in Goodsprings.
One is in a brown house located south of the saloon, not far from a wrecked travel trailer and pickup truck. The house has a couple of beds, a refrigerator and other storage containers. Haven't tried any containers out yet to see if they're safe. Easy Pete went into the house to sleep on one of the beds, but he didn't seem to mind my using the other one. No well rested bonus for sleeping there, so it isn't my bed.
Also, there's mattress you can sleep on in the gas station where you meet Ringo. There are also a few containers in here.
I'll bet I can get a house of my own by helping the town beat the Powder Gangers, similar to getting the Megaton house by defusing the bomb in FO3. Will try later on tonight.