Many references to distances are from actual dialogue, so all the usual players would appear to be extremely local - next-door neighbors to Earth, really, sharing the exact address.
Modern onscreen graphics tend to reproduce the views of the Star Charts booklet by Geoff Mandel: this layout of local space is seen in DS9, VOY and DSC all, and is the basis of some location ideas in ENT as well, even if only implicitly. It's also used in the ST Online game and in the movie Into Darkness, among others.
The view above is an earlier take, Andrew Probert's way of paying homage to earlier fan maps (the most famous one of which was by the same Geoff Mandel). It also seems to reflect actual art department ideas, though - or at least the art department, which famously maintained a coarse map on its wall, seems to have agreed with Probert's take here on many things. For them, in any map where the galactic core is up, the Klingons are to the lower right and the Romulans to the upper right, and the Cardassians to the left. This isn't at odds with Probert's art above yet, although he doesn't include Romulus (for whatever reason - perhaps he only listed UFP worlds and considered the Klingons UFP members) or Cardassia (for the obvious reason of it not having been invented yet).
But Probert's art isn't "right". The stars with names taken from the real world aren't at their correct positions at all. Some of this Probert inherited from Mandel's earlier maps where there was an unfortunate coordinate translation error that rotated an otherwise realistic placement of stars. Some is due to artistic liberties taken by Probert. The location of Andor or Andoria could be either of those - the older maps had it at Epsilon Indii, to honor a choice made in the early Star Fleet Technical Manual by Franz Schnaubelt, but Mandel later put it at Procyon (which is 11 ly away). Now, there's no star named Epsilon Indii, but there is Epsilon Indi, which is 12 ly from Earth.
Why the change? Perhaps because Mandel would have been aware that Epsilon Indi already played another role in Trek lore, a victim of the Triacus marauders in TOS "And the Children Shall Lead" - the failure to mention Andorians in that episode might have been damning. But Mandel then slapped the Epsilon Indi identity to another Trek location, Draylax... But I digress.
Vulcan in basically all maps resides at 40 Eridani (a location favored by fandom since time immemorial, and at the quoted 16 ly distance). That Probert's map above would have it at the wrong spot relative to Earth is possibly due to Probert quoting Mandel's earlier map, the one with the coordinate rotation error. And Andor could be rotated to that funny and inappropriate place the same way, assuming it was indeed Epsilon Indi in Probert's mind still.
So, to recap: there's a modern understanding of which stars are the Andorian and Vulcan homestars. There's no direct dialogue reference to either, though, nor explicit graphics equating them with those stars. There are, however, many explicit references to Vulcan being exactly 16 ly from Earth, reinforcing the idea that it is 40 Eridani. But there's no reference to Andor(ia) being 11 ly away - this is mere conjecture from the conjectural idea that it would be orbitin the real Procyon.
Timo Saloniemi