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WIKIPEDIA says
Because of interstellar dust along the line of sight, the Galactic Center cannot be studied at visible, ultraviolet or soft X-ray wavelengths. The available information about the Galactic Center comes from observations at gamma ray, hard X-ray, infrared, sub-millimetre and radio wavelengths.
Coordinates of the Galactic Center were first found by Harlow Shapley in his 1918 study of the distribution of the globular clusters. In the equatorial coordinate system they are: RA 17h45m40.04s, Dec -29° 00' 28.1" (J2000 epoch).
Distance to the Galactic Center[edit]

The exact distance between the Solar System and the Galactic Center is not certain. The latest estimates from geometric-based methods and standard candles yield distances to the Galactic Center between 7.6–8.7 kpc (25,000–28,000 light years).[6][7][8][9] An accurate determination of the distance to the Galactic Center as established from variable stars (e.g., RR Lyrae variables) or standard candles (e.g., red clump stars) is hindered by countless effects, which include: an ambiguous reddening law; a bias for smaller values of the distance to the Galactic Center because of a preferential sampling of stars toward the near side of the Galactic bulge owing to interstellar extinction; and an uncertainty in characterizing how a mean distance to a group of variable stars found in the direction of the Galactic bulge relates to the distance to the Galactic Center.[9][10]
The nature of the Galaxy's bar which extends across the Galactic Center is also actively debated, with estimates for its half-length and orientation spanning between 1–5 kpc (short or a long bar) and 10–50 degrees.[8][9][11] Certain authors advocate that the Milky Way features two distinct bars, one nestled within the other.[12] The bar is delineated by red-clump stars (see also red giant), however, RR Lyr variables do not trace a prominent Galactic bar.[9][13][14] The bar may be surrounded by a ring called the "5-kpc ring" that contains a large fraction of the molecular hydrogen present in the galaxy, as well as most of the Milky Way's star formation activity. Viewed from the Andromeda Galaxy, it would be the brightest feature of our own galaxy.[15]

Approximately 25,000 light years, in layman's terms.

The Galactic Center is the rotational center of the Milky Way galaxy. It is located at a distance of 8.33 ± 0.35 kpc (~27,000 ± 1,000 light-years) from the Earth. http://en.wikipedia.org/wiki/Galactic_center

I just found out on one of the science channels that to reach light speed (186,000 miles per second) using our current technology in propulsion it would take 7 years to reach this speed, and twice this to bring to a stop. Current means of propulsion is based on action/reaction.  In space, its a void, this means all energy to reach this speed must be initialized during the launch because once in the void of space you can not speed up and the only way to slow down is enter another gravitional/matter element. so.. If you launch and are off 1/1000.000 degree by the time you reach the distance of 75 light years you would be off target by several billion miles. Not to mention, you would be already dead and turned to a pile of dust.  Your body would never handle the escape velocity, the pressure would make mush of your organs. -- In otherwords, we are stuck here.  The great plan had arranged it that way, I believe in life on other planets but i also believe in science and science principals, they are stuck there too!  LOL!  Who knows, maybe someday we will have a star trek transporter that will disassemble your atoms and restructure them light years away from here. You may be half a fly though. Not to mention, according to Einstein, there is no velocity beyond light speed and most of the places we want to go is at least 4.3 billion light years away so we would certainly need this transporter and we would be 'disassembled' for 4.3 years or 23 trillion miles just to get to the closest  life possible star. I don't think we gunna do that in our lifetime. :)

Wow, I better get a vehicle with better mpg, huh?