Earth is in the second largest galaxy of the Local Group - a galaxy called the Milky Way. The Milky Way is a large spiral galaxy. Earth is located in one of the spiral arms of the Milky Way (called the Orion Arm) which lies about two-thirds of the way out from the center of the galaxy.

Here we are part of the solar system - a group of nine planets, as well as numerous comets and asteroids which orbit the sun.
The Solar System has been measured to be about 28,000 light years from the center of the galaxy, and about 20 light years above the galaxy's equatorial plane.

The Milky Way Galaxy belongs to the Local Group, a smaller group of 3 large and over 30 small galaxies, and is the second largest (after the Andromeda Galaxy M31) but perhaps the most massive member of this group. M31, at about 2.9 million light years, is the nearest large galaxy, but a number of faint galaxies are much closer: Many of the dwarf Local Group members are satellites or companions of the Milky Way.

The two closest neighbors, both already mentioned, have only recently been discovered: The nearest of all, discovered in 2003, is an already almost disrupted dwarf galaxy, the Canis Major Dwarf, the nucleus of which is about 25,000 light-years away from us and about 45,000 light-years from the Galactic Center. Second comes SagDEG at about 88,000 light years from us and some 50,000 light years from the Galactic Center. These two dwarfs are currently in close encounters with our Galaxy and in sections of their orbits situated well within the volume ocupied by our Milky Way. They are followed in distance by the more conspicuous Large and Small Magellanic Cloud, at 179,000 and 210,000 light years, respectively.

Actually, there is no real 'center' of the universe that one can define since there is no tremendous difference in the cosmic microwave background radiation density throughout space. It basically means that aside from planets, stars, galaxies, etc. space is exactly the same (or close to it) at all spots in such a manner, no 'center' can be defined.

We only know our position relative to other galaxies, but we do not know how they are scattered relative to the universe as a whole.
Source(s):
http://messier.obspm.fr/more/mw.html

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