This house in Japan includes quite an aspirational example of an indoor rock garden, but that's sometimes the best inspiration, isn't it?
Designed by Suppose Design Office, the house is situated on a small lot that doesn't include much outdoor space. Instead, the client wished to have an indoor room dedicated to a "garden".
The same could be done in a small apartment, albeit on a more modest scale. Imagine tending a small rock garden in aquarium, a handmade wooden tray, or out on the balcony - even in a nonworking fireplace!
Images: Suppose Design Office

Shaw's Original Fir...
Like the idea of using a non-working firebox. You could tuck a light up above and grow some happy plants!
Now I almost regret that we use our fireplace all.the.time.
I love the Japanese inspired works. I found a Jolie Papier wallcovering with a Bonsai plant on DecoratorsBest that's astounding!
Lovely.
But the problem is the dust... dusty indoor gardens are simply gross, I think.
The rock garden is great, but the view of the toilet from the dining table would spoil my appetite. :/
There was one in our house when we bought it (in the form of a built-in plastic tray by a window in the dining room). We ripped it out the same day we took possession of the house because
a) we have little kids and the rocks would never have stayed IN the garden and
b) the previous owners' cats had been peeing in there. We have a cat too and won't ever do an indoor rock garden because he doesn't need a huge, permanently installed litterbox.
I agree with Evergirl about the dust. I have a little tray of rocks and bamboo that's very cute, but it requires frequent dusting and can get pretty gross. Not a problem with a small tabletop item, but I can't imagine dusting off thousands of rocks every month :S
I have to admit it looks beautiful, though. I'd love to have an indoor garden, but maybe filled with tropical plants.
If there is drainage below, you could just spray down the rocks with the shower head to clean them. That would be convenient since it's right outside the bathroom, and there are plants that need to be watered anyway.
why exactly can you see the toilet from anywhere in the house? maybe they should plant a large bush in front of it. heh.
I think in a previously existing western style home, this would be difficult to pull off attractively. You need a fair amount of space. (In the example, defined by glass walls and the aisle space next to them.) It has to be somewhere off any traffic pattern, so maybe along a wall or next to windows you don't want to stand right by... It needs a sense of containment with logical boundaries. It needs to be carefully planned so the rocks or gravel or plants or whatever are in appropriate scale. And maintanance is an issue, as others have suggested.
One option might be a rectangular flat tray with straight (boxy) sides holding an array of polished river rock on a table. If you need plantlife, a bonsai or potted orchid might be added in the tray, off center. Maybe a grouping of three nicely shaped "mountain" rocks instead, like little islands... There should be nothing else on that table, or the effect would be lost.
Different notions of privacy in different places perhaps! Love Japanese architecture generally though, it has such a simplicity and purity like in the house shown here. Indoor gardens like that can be really nice, here especially it blurs the distinction between indoors and outdoors.