Up until now, I'd never realised that I can apparently put my armour on a mannequin for storage and display; I've never really needed one, but I guess it would look nice

So where can I find these? (I don't have DLC's, by the way, in case they're a DLC-only thing)

I believe these are add ons for most, if not, all homes.

Aside from the ones you get with Hearthfire, you also get Mannequins in all vanilla houses except for Breezehome. No houses have anywhere near the number of Mannequins you can have with Hearthfire houses, though.