At what distance from Earth would our Sun be the same apparent magnitude as the next brightest 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.