I've recently started a barbaric character (Melakaar Jenasari) and was wondering if there was any cave with a alchemy lab I could make his home that would be safe for ingredient and food storage.I'm not sure if this is possible so if anyone knows for sure it would be much appreciated. Also, I don't have hearthfire and play on 360.

A lot of these locations are safe and have alchemy stations.

http://www.uesp.net/wiki/Category:Skyrim-Places-Safe

A Barbaric Alchemist?

Yeah, its the only crafting im taking so he's kinda barbarian/hunter/native American Wildman type of build.

Southfringe Sanctum is a little remote, being almost as far south as you can go past Helgen/Fort Neugrad, but isn't too cavernous and has plenty of storage, is well lit, and has 2 alchemy labs.

If you prefer something a bit darker and more northern, Harmugstahl is a cave/fort in the Reach near Dragonstooth Crater with a lab.

Those are your best bets for an easily accessible base, where the cave storage won't respawn if you're gone. There are some better and cosier caves but not really that many that don't respawn.

Thanks everyone!very helpful info and links.