Though the original question was for 10.0, I have updated the code below for 10.3.1.
Copy paste this into the python window in arcmap to create the RasterCenter function:
import arcpy, os
def RasterCenter(raster):
#raster: string reference to raster
raster = arcpy.Raster(raster)
fcname = "{}_center".format(os.path.basename(str(raster)))
x = raster.extent.XMin + (raster.extent.XMax - raster.extent.XMin)/2
y = raster.extent.YMin + (raster.extent.YMax - raster.extent.YMin)/2
featureclass = arcpy.CreateFeatureclass_management("in_memory", fcname, "POINT",spatial_reference = raster.spatialReference)
with arcpy.da.InsertCursor(featureclass, ['SHAPE@XY']) as cursor:
cursor.insertRow(((x, y),))
mxd = arcpy.mapping.MapDocument("CURRENT")
df = arcpy.mapping.ListDataFrames(mxd)[0]
arcpy.MakeFeatureLayer_management(featureclass, fcname)
layer = arcpy.mapping.Layer(fcname)
arcpy.mapping.AddLayer(df, layer)
Then, you can use the python window to create your feature class by calling
RasterCenter("<reference to raster">)
So, for example, if you have a raster named DEM, you call RasterCenter("dem") in the python window, and it will add a layer named "dem_center" with a single point at the center of the raster. The layer is stored in memory, so if you want to keep it, export it.
To go one step farther, you can save the script to a .py file and place the .py file in the search path for python. e.g. save it as RasterCenter.py and place it in PYTHONPATH (normally the spot for this is C:\Python26\ArcGIS10.0\Lib)
Then you could do:
import RasterCenter
RasterCenter.RasterCenter("<reference to raster">)