There's no fun in having mead barrels in your homestead's basemant without empty bottles to be filled.

I do know they're found in bandit caves, I just don't know which one.

I've seen tons of empty wine bottles, even some skooma bottles, but never mead bottles.

Edit: most bandit caves have at least a couple of empty wine bottles. These two locations -

have quite a few off of the top of my head.

Can empty bottles actually be filled?

There are a bunch in the Winking Skeever in Solitude, and on the shelves behind Vitoria Vicci at the East Empire Company.

Right, there's no item actually called empty mead bottle, I don't think.

Which you'd have to steal, I figure.

Morvunskar has 105 bottles for youto loots

Most Forts (and some bandit hideouts) have a large Beer Hall room with these mini Beer tables(not sure what to call them.) most of these have beer on the top and empty bottles on the lower shelves