So I just started playing NV on hardcoe mode. I need a house or other storage area that is safe and I can store all my extra food and ammo in. Any suggestions?

http://fallout.wikia.com/wiki/Fallout:_New_Vegas_player_housing

Wolfhorn is popular: http://fallout.wikia.com/wiki/Wolfhorn_Ranch

If you need something right away, the abandoned shack is very close to Goodsprings: http://fallout.wikia.com/wiki/Abandoned_shack_(Fallout:_New_Vegas)
I haven't tested the containers in either building, so I can't vouch for their safety. Maybe someone else can?

EDIT: looks like the links might be malfunctioning. To find the abandoned shack, just make your way to the Yangtze Memorial. You can see it from there.

The robot's shack in Goodsprings has safe storage and a you can sleep in, I always stay their early in the game and use the storage.

Jenn