At what distance from Earth would our Sun be the same apparent magnitude as the next brightest star in the sky? When I stand outside looking at the night sky, to my untrained eye, everything except the moon looks like a star.  I know intellectually that some are planets circling our sun, and some are entire galaxies far away, but they all look basically the same.

How far out do you have be be from our sun for it to appear the same as any other 'star' in the sky? 

Edit to clarify

As we migrate out through the solar system, when we look up to the sky the sun will get dimmer the farther away we get. On earth there is no doubt which star is our sun. 

As we occupy bodies in the solar system farther from the sun, where will we be when the sun appears to be the same brightness as any other star in the sky?
One way to answer would be to consider the brightest star in our sky (other than the Sun), which is Sirius.  Then determine how far you would have to be from our Sun for it to be as bright as Sirius is from here.

That turns out to be 1.8 light years.  That's not even halfway to the nearest star, so if you're in any other star system, then our Sun is just another star.  If you're anywhere in our solar system, even way out in the Oort cloud, then our Sun is way brighter than anything else.