What specific parts of the Milky Way do we see when we look up? I know we can't see the center.  But do we see any of the central bulge?  Are we just seeing nearby stars in the Orion Spur where we are?  In the Sagittarius Arm?  In the other direction, are we seeing any of the arms further out from ours?  Where are the dust clouds we see, in relation to these arms?
But do we see any of the central bulge?


With the naked eye and a dark sky, the galactic center is brighter than other areas of the galactic plane.  Some of the light from that region does make it to earth to make that direction identifiable. 

If you look at the ESO night sky composite from Brunier and Tapissier (which is approximately what someone could see with the naked eye given dark skies and good viewing), you can see that while the galactic center is brighter, other directions along the plane seem fairly similar.  That makes it very difficult to say what fraction of scattered glow is coming from one arm or another.  It all just blends together.


https://www.eso.org/public/news/eso0932/


  If all we can see are stars in our galaxy that are relatively close to us, then the Milky Way should look relatively uniform, right?


Not necessarily.  The visible part of the galaxy is relatively thin.  It doesn't have a fixed distance, but a commonly quoted one is 1000ly.  That means that even if light were magically cut off at 3000ly or so, it could appear non-uniform.