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 Triangulum galaxy, aka Messier 33, has the distinction of being the farthest object you can see with the unaided eye. But you'll need a dark site to catch a glimpse of it.
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.
The Eagle Nebula - aka Messier 16 or M16 - is home to several well-known cosmic structures, including the stunning Pillars of Creation and Stellar Spire.