Neighbours across the outer space :

Comet

Mars

Venus 

Near Earth Objects

Proxima Centauri

Cannis Major Dwarf 

Our planet Earth is not alone. It has many neighbours in the outer space.
The nearest neighbour to Earth is it's very own natural satellite, the Moon.

The second nearest neighbour to Earth is the planet Venus (At times) which is at a distance of about 38 million kilo meters at the closest point and 261 million kilo meters at the farthest point.

On the other hand, Earth is also surrounded by Mars, which is at a distance of 54 million kilo meters at the closest point and 401 million kilo meters on the farthest point,

Planet Earth also has millions of Near Earth Objects (NEO's) as it's neighbours.

The nearest star to Earth is our Sun.The closest distance between Earth and Sun is about 147 million kilo meters at the closest point.

The second nearest Star to Earth is the Proxima Centauri which is 4.23 light years i.e., around 4*10^16 meters.

Our planet is located in the Milky way Galaxy. The nearest Galaxy to Earth is the Cannis Major Dwarf (Located within Milky way itself. A galaxy within a Galaxy) (Yes, not Andromeda) which is about 25,000 light years from Earth.

The nearest Black hole to Earth : The V4641 Sagittarii, a micro-quasar which is about 1,600 light years from Earth.
(Some say that the speculations on the distance of V4641 Sagittarii are wrong and it is at a distance of about 25,000 light years).

Apart from all these celestial neighbours, we've even got comets.

Moon