Which constellation is up at what time varies with the seasons. If they're up by day, you don't see them. (If you care why they change, look up sidereal day vs synodic day).
Depending on your latitude, some constellations may never set. These are called circumpolar. If you're on the equator, almost nothing is circumpolar (and you see almost the whole sky). If you're at a pole, almost everything is circumpolar (and you never see the other half of the sky).*
At my latitude, the Dippers are circumpolar, and I never see stars near the south celestial pole. ('The Wain' referred to in _The Lord of the Rings_ is the Big Dipper. A wain is a wagon.)
*I'm leaving out some complications; my description is inexact.
There's a 26,000 year cycle, traditionally called precession of the equinoxes, in which the direction the earth's axis is pointing with respect to the stars, spins around in a circle. Right now the axis is pointing at Polaris in the north and nothing in the south. There isn't always a north pole star, and when there is it isn't always as close to the pole as it is now, and it isn't always Polaris.
Tolkien's elves, in his chronology, would have seen times without Polaris as a pole star.
Inner Planets (Mercury, Venus) only get visually so far from the Sun -- which is why Mercury is often not all that easy to see, and Venus is either a Morning Star or an Evening Star. Outer planets can be anywhere along a path through the sky called the ecliptic. They can be up at any time of day or night, depending on where they are in their orbits.
The ancients were aware of seven celestial bodies beside the stars: Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn. They couldn't see Uranus, Neptune, any asteroids, Pluto, etc.
(In Tolkien's cosmology the whole fashion of the world -- yea, the universe -- was changed at the Fall of Numenor. Evidently before the Earth was a disk, the Sun and Moon revolved around it, and Venus was a Silmaril. When I read the Silmarillion I studiously ignore everything I know about physics. It seems best viewed through the lens of legend.)