Moving / offsetting point locations using ArcPy or ModelBuilder?

This code should do it using the SHAPE@XY token that came with arcpy.da.UpdateCursor in ArcGIS 10.1.

import arcpy
# Set some variables
fc = r"C:\temp\test.gdb\testFC"
fc2 = r"C:\temp\test.gdb\testFCcopy"
xOffset = 0.001
yOffset = 0.001
# Code to make a copy which will have its coordinates moved (and can be compared with original)
if arcpy.Exists(fc2):
    arcpy.Delete_management(fc2)
arcpy.Copy_management(fc,fc2)
# Perform the move
with arcpy.da.UpdateCursor(fc2, ["SHAPE@XY"]) as cursor:
    for row in cursor:
        cursor.updateRow([[row[0][0] + xOffset,row[0][1] + yOffset]])

The coding pattern used here came from ArcPy Café.

I credit @artwork21 for leading me to my final solution. I actually found a nearly complete script in the ArcGIS 10.0 online help article called "Calculate Field examples", listed under the subcategory "Code samples—geometry" and "For a point feature class, shift the x coordinate of each point by 100"

The final script that I used within the ModelBuilder "Calculate Field" tool was:

Expression:

shiftXYCoordinates(!SHAPE!,%ShiftX%,%ShiftY%)

where ShiftX and ShiftY are variables (as parameters) defined on the ModelBuilder canvas.

Expression Type:

PYTHON_9.3

Code Block:

def shiftXYCoordinates(shape,x_shift,y_shift):
   point = shape.getPart(0)
   point.X += float(x_shift)
   point.Y += float(y_shift)
   return point

Since all models work on a selected set, you should also be able to create this as a generic tool that will work in conjunction with other models/tools in other modelbuilder sessions. The very simple model I created (as a "plugin" to other models to shift coordinate values) looks like this. That way I can control the shift on a per-selection-set basis (as defined in other models):

It worked like a charm, thank you all for your input!

You may also use this field calculator script to move feature locations:

def XYsetVALUE( shape, X_value, Y_value): 
  myMoveX = 0.001
  myMoveY = 0.001
  point = shape.getPart(0) 
  point.X = X_value + myMoveX
  point.Y = Y_value + myMoveY
  return point 

XYsetVALUE ( !SHAPE!, !X_COORD!, !Y_COORD! )

You could include an extra Calculate Field method within your model using the function above.