The only magical creatures we see in the novels that Muggles are incapable of seeing are the Dementors and the Thestrals (most likely - we never see Muggles near them).
The Dementors are dark, evil creatures, the stuff of nightmares. They are the shadows under your bed and the things that go bump in the night. They are the cold chill on your spine when you awaken, screaming, from a nightmare. Muggles cannot see them, but they feel the effects well enough. Their invisibility to the mundane world is most likely part of their powers, like the soul-stealing 'kiss' and their happiness-draining aura.
Thestrals, on the other hand, have the magical ability to remain unseen unless the observer has witnessed and understood death, personally. We never see a Muggle who sees one, or who is in the position to do so, so we don't know if Muggles who've seen death can see them.
There are no other magical creatures in the series which Muggles can't see. It's mentioned that they CAN see giants, dragons, etc. Non-human creatures such as house elves and goblins have their own ways of going unseen, or of blending in.
Structures like Diagon Alley and Platform 9 3/4 are hidden by magic.