From Pluto there would be no noticeable shift in the shape of the constellations. From the nearest stars, there would be a visible shift in many of them since a good many of the brightest stars are closer than 100 light years and a 4 light year shift would produce at least a 2-3 degree shift about as big as 4-6 times the full Moon. Moving to the center of the Milky Way changes everything because all the stars you see are within a few thousand light years of the Earth and the galactic center is over 25,000 light years away. The stars we see in the sky within a region of space 2000 light years across would subtend an angle of about 5 degrees across from the center of the Milky Way!!