You should try that downed airplane shack near the cross at Yangtze Memorial, right on the left of where you're looking when you fast travel there (really only about 20 steps away from where you spawn). I've been using it for awhile and haven't lost one item I've put in there. It has a bed, reloading bench, ammo crate, and first aid kit inside. Plus it just makes you feel like a badass mercenary to use a shack in the middle of the desert rather than a motel room.
That's the place I go with! What's also great is that there are three Xander Roots to pick up, one between the memorial and the shack (kind of hard to see, it's placed lower
into the ground), and the other two next to each other by a small rock on the downslope in front of the door.
The problem with that shack are the Giant Radscorpions that live near it. They can be a real pain when low level. They have a bad habit of sitting outside the door.
That's why I chose that place, along with the ammo bench inside. I end up going through the whole Scorpion Gulch and basically just treat it as an opportunity to harvest even more radscorp glands.
I now have 2 giant ones and two small ones that are literally at the fast travel spawn, so I always fast travel there with my hunting shotgun at the ready.