Is it okay to take that pretty nest as a sample or a show-piece to put in a personal balcony or a garden?
This can be a simple question of size. A large nest, like an eagle's nest, is of course too impractical to take away! but, a really small nest is generally built in a season. Birds are used to that. The smaller the nest, the more really good places there will be to build it, from the bird's point of view... unless nest-building habitat is really scarce, in which case, leave it! to be used or ruined or re-used as 'nature' would have it.
Also very important: if it is a protected or endangered species' nest, you shouldn't even go near it, much less take it away with you. As an example, California Condors tend to be very easily 'spooked' off the nest when brooding eggs or young... which can lead to loss of the chick or viable egg.
And also important: for some species, if it is not a highly-constructed nest like that of a typical songbird, which nest is woven together or otherwise wholly made-on-site, the nest can be very scarce as resources go. Cavity nest sites, for instance, are re-used by many species because such cavities are both rather secure locations, and are also scarce or in short supply - or, require extensive labor to chisel and hollow out.
Another point is, some species have only hollow stubs to nest in - and, for some, the supply of (suitably sited) hollow stubs, or stubs of trees that could be hollowed out with some effort (but for weaker species, not too much i.e. partially rotted softened wood) ... is quite scarce, and a drastic limiter to that species' continued abundance. I think the American Wood Duck is a good example of this. They could be more abundant if there were more completely undisturbed (they are very shy and nervous as a consequence of being nearly exterminated/extincted by overhunting etc.) suitable stubs of softened wood near suitable bodies of water... but such rotted wood is eliminated by forestry practices etc.
So in sum:
Leave rare/endangered/shy species' nests alone and untouched... you could be doing them a great favor, and/or saving yourself from a punitive visit from a Warden or police.
And leave stubs and hollowed-out nests where they are.
And don't take anything large, of course!