I want someplace with no cap on mounts and pets. I'm thinking a medium sized cavern, hole in the roof for sunlight, a tree or two and shallow water. (Seen in many delves and dungeons) Here's where it gets interesting. Around the perimeter of the cavern are about 10 or 12 daedric portals. Each one has a shimmering image of the "room" inside. Each room is themed for location or element. (snow, lava, dwarven/clockwork, farm/stable for barnyard animals, forest, desert, daedric, etc...) Stepping into a portal would open the door to that exhibit room.
I have very little programming knowledge. But, if I understand correctly, the animations are the issue. Like having too many torches, the light sourcing works but the flame animations sometimes don't show up. If each room were it's own cell, loaded only when you enter, like an interior, this should allow more animations for pets and mounts per room. Then you could display all your animals.
As for location, I was thinking it could be a Daedric portal that is a housing furniture item. You place it in one of your houses and when you use it, you are transported to the central cavern.
Backstory is that it is a daedric "pocket" realm, belonging to a low level daedra that was fascinated with all the varied creatures on Nirn and was collecting them for study. Maybe even make a quest to track down the daedric collector and defeat it. The reward is the portal housing furniture item.