The Andromeda galaxy is the closest big galaxy to our Milky Way. At 2.5 million light-years, it's the most distant thing you can see with the eye alone.
The Great Rift or Dark Rift is a darkened swath of the Milky Way where new stars are forming. It's best seen from a rural location away from light pollution.
Omega Centauri is the Milky Way's largest globular star cluster and contains about 10 million stars. It's even visible from parts of the Northern Hemisphere.
The Beehive cluster is an open star cluster that lies near the center of the constellation Cancer the Crab. It goes by many names, including Praesepe and M44.