Wasn't there a comment in Balance of Terror about the Romulan's lacking warp drive back during the war?
The episode gave three key specs about the old war, none of which touched upon warp drive:
1) fought with primitive atomic weapons
2) fought in primitive space vessels
3) (apparently as the result) there was no mercy given, no prisoners taken, no ship-to-ship visual communication
Later on in the episode, the heroes fight a modern Romulan vessel that evades them at warp three, even though Scotty claims "their power is simple impulse". This in no way establishes anything about the old war a century prior, as Scotty didn't make his claim without first having a look at the ship in question - he wasn't basing his (mistaken?) assessment solely on historical records or anything.
Some fan sources did interpret this all as the Romulans not having had warp drive until late in the game - perhaps as late as the second season of TOS! But onscreen Trek has never supported the idea that Romulans would have lacked the secret of warp at any point of their history. For all we know, they were capable of warp long before they even left Vulcan.
Curiously, we never quite learn who won the old Romulan war. The Neutral Zone between the powers suggests a stalemate conclusion to the conflict...
Suppose a typical Federation citizen wants to travel to Bajor or some place like that from Earth to see antiquities in museums. How long would it take?
DS9 was pretty consistent about this only taking about a week, at least with Starfleet vessels and craft.
Then again, DS9 also suggested that Bajor wasn't really all that distant a place. It just happened to border on the territory of an unyielding enemy, in a direction where the UFP hasn't been able to expand much, so it certainly qualified as "frontier".
Sometimes our DS9 heroes discussed getting from Bajor to places other than Earth. In "Fasctination", it was 300 ly from Bajor to Regulus III; since Regulus is a real place about 80 ly from Earth, at least in our universe, Bajor would probably in turn be about 150-250 ly from Earth, if we accept that it is "to the left" of Earth and recognize that Regulus is "to the lower right". A couple of hundred ly in a week is average going in 24th century terms, and Archer in his warp 5 ship did something quite comparable in "The Expanse".
We aren't really into major complication or contradiction territory here, then. It's just that some parts of the amoeba-like UFP appear to be a lot farther out than Bajor. Jouret of "Best of Both Worlds" fame was another frontier location, an "outermost colony", and it again took at most a week to move the action from there to Earth, although this time at high warp in a very fast starship.
We don't know how long it really took for the comparable fight to move from the frontier colony of Ivor Prime, outside UFP borders just like Bajor (and apparently accompanied by a Deep Space station just like Bajor), to Earth in ST:FC. The fight moved from Ivor to Typhon in an unknown amount of time, and Typhon was mentioned in TNG "Cause and Effect", so we have some ballpark data there. Unfortunately, some of it gives minimum estimates (at least hours from Ivor to Typhon, or else our E-E heroes would not have dreamed of joining the fight), the rest maximum estimates (a 23rd century starship took at most three weeks to reach Typhon from Earth in the TNG episode), so it cancels out.
We do end up with a general feeling that the borders of the UFP are about a week away from Earth for anybody bothering to make the effort, save for individual special cases: some colonies or member systems may be thousands of lightyears away and probably take months to reach, while the RNZ may scrape really close to Vulcan and Earth at its closest point.