Furnishing recipes seem to drop pretty much anywhere - I presume they are more prevalent in their respective racial zones, but you can loot them from any chest / wardrobe / cupboard etc in game.
Some drop primarily from mobs, such as the Deadric plans that drop from any Deadra mobs throughout the world, and possibly more commonly from Daedric themed dungeons.
Certain items are looted from pick-pocketing / murdering NPCs in different zones, ESO Fashion should give you info on that.
This I *think* is an extensive list of items and where to find them: https://eso.mmo-fashion.com/furnishings
Outlaws - Gambling Dice
Guards - Bounty Posters
Beggars - Bread morsels, sometimes mugs
Drunks - Mugs, liquor bottles
Scholars - stack of papers, quills
Those are just the ones I've personally gotten. Also anyone in Vvardenfall can drop house outfit motifs.
Edit: I'm not 100% sure but I think they changed the skooma bubblers and they don't drop anymore.
You can get an hourglass recipe in the gold coast from priests (Kvatch).
You can get coffin and coffin lid recipes from vampires.
You can get wood elf throne recipes from nobles in Eldenroot.
You can get breton throne recipes from nobles in Wayrest.
You can get orc throne recipes from nobles in Orsinium.
You can get a writing desk recipe (if I recall) from temple priests in the starting city in Summerset (I forget the name).
Get the dark brotherhood passive that allows you to interact with Remains Silent to get a free item once a day that may include furnishings such as candles, hearts, and I forget the last item)
Doing Ashlander dailies in Vvardenfell gives a chance to get a rare red crystal furnishing (I forget the name).
There are others, but I can't think of them at the moment.