The storage is safe in your quarters after completing the quest. There is another bedroom there, that ALSO has safe storage, though you can never sleep in the bed. If you are leery about the storage in either room, take all, from every container, replacing that with a single arrow. Leave for four days, the city I mean, then come back. Then you will rest easy knowing that it is a guarantee.
Thanks (: I will test out Dementia's quarters, but I'd assume that there's safe storage there as well.
As for White Stallion Lodge, it's a fantastic place. Caius loves sitting on the veranda, watching the sun set, taking a dip in the river and drinking way too much mead. He keeps all of his food with him, just so he doesn't lose it
his house mate is hardly ever there, as well!