Actually, that DS9 map comes with a scale, sort of: it shows both Bajor and Cardassia, and the distance between them is roughly known in terms of travel times at least. In scale with that, the Romulan bird symbol isn't too far away from Cardassia.
It should be noted, though, that the map does not exactly show Romulus. It just shows the Romulan symbol, at a distance that would amount to about a hundred lightyears if we accept Bajor and Cardassia as being 5.25 ly apart as intended by the makers of that map (see p. 3 of the DS9 Tech Manual). Perhaps it indicates the current position of Romulan forward headquarters?
Similarly, the map does not feature Earth. But we could assume Earth to lie in the middle of the map, with Dominion conquests now reaching "beneath" it towards the right of the map and bordering on Romulan space just like the plotlines indicate. This is how the map was interpreted for Star Charts
and for ST Dimension both.
In any case, that map is an example of the "small Federation" trend prevalent in the making of DS9. The trend would indeed allow Romulans to quickly hop to Cardassia even if basically the entire bulk of the Federation lay between them. That bulk would just happen to be a compact little sphere a couple of hundred ly across at most, with Picard's "8000 ly" claim from ST:FC then referencing some fairly irrelevant outermost holdings.
Even traveling through the very heart of the Federation might be doable without cloaks, as we often see our heroes encounter intruders rather close to Earth. But enter cloaks, and a Romulan or Klingon conquest fleet has every dramatic excuse for nonchalantly penetrating the Federation while heading for some other victim.
The anti-cloak systems indicated to be in place by "Face of the Enemy" may be highly local, available at the hottest potential border-crossing sites only. After all, Romulans continue to frequent space outside their Star Empire after that episode...