Setting to open new TextEdit document window in center?
It seems that TextEdit hardcodes the position for new document windows, and it's not possible to tweak this behaviour using defaults write to modify TextEdit's Preferences. See this old post from Apple Discussions:


  The current version of TextEdit does not maintain a preference in the com.apple.TextEdit.plist file concerning window placement for the document window. What appears to be missing in the TextEdit preferences file is an 
   NSWindow Frame property for the document window itself.


To change the default position of new TextEdit documents there's really only one solution: write a custom AppleScript that can open a new document at your preferred location centered on the screen.

tell application "Finder"
    set screen_resolution to bounds of window of desktop
end tell

tell application "TextEdit"
    set screenWidth to (item 3 of screen_resolution) - (item 1 of screen_resolution)
    set screenHeight to (item 4 of screen_resolution) - (item 2 of screen_resolution)
    set screenCentreX to screenWidth / 2
    set screenCentreY to screenHeight / 2

    activate
    make new document

    set defaultBounds to bounds of front window
    set x1 to item 1 of defaultBounds
    set y1 to item 2 of defaultBounds
    set x2 to item 3 of defaultBounds
    set y2 to item 4 of defaultBounds
    set w to x2 - x1
    set h to y2 - y1

    set centreBounds to {screenCentreX - (w / 2), screenCentreY - (h / 2), screenCentreX + (w / 2), screenCentreY + (h / 2)}

    -- "set position" does not work, so we need to fall back on "set bounds"
    -- https://stackoverflow.com/q/12803847/190298
    set bounds of front window to centreBounds
end tell