A Danube Class starship was seen to be carried around by the Enterprise-D as an auxiliary vessel in "Timescape"[TNG7]. Used by a few bridge crew officers to attend a conference, the vessel appeared no different than any other Danube.
In the episode, a temporal anomaly causes time to move signficantly faster for the starboard warp systems . . . the runabout comes to a dead stop because the starboard engine fails. It's soon discovered that the failure is a result of the starboard engine running out of fuel . . . the starboard antimatter pod is found to be empty. The temporal anomaly meant that the starboard nacelle had been in continuous operation for 47 days.
This implies a few odd things. For one, it suggests that there is a dual-core system in place on runabouts. After all, for starboard antimatter to be empty and for the nacelle to have functioned for 47 days, there must have been a core which was operating to produce power for that amount of time. Otherwise 47 days worth of antimatter would've had to have been fairly suddenly run through a single warp core which was not functioning at that rate. This would be akin to putting an entire tank's-worth of gas in your car's engine cylinders all at once. However, it's likely that other discussions on runabout warp cores may suggest that there is just one, so perhaps another explanation must exist.
More importantly for our purposes, though, this gives us a figure for the endurance of the runabout. It is not known if the runabout's tanks were full or near-empty when it departed the Enterprise-D, nor is the speed of the vessel known, but a vessel endurance of 47 days at warp velocity is established here. At warp one this would give a range of 0.129 light-years. But the runabout was attempting to locate the missing Enterprise, suggesting higher speeds in use.
In "Dax"[DSN1] a well-prepared group must make an escape from the station. Kira points out that they probably have a vessel capable of outrunning a runabout handy. Sisko orders Kira to determine which ships docked at the station have a high warp capability ... her search includes ships capable of "warp five or more", suggesting that the runabouts are capable of at or near warp five, maximum.
Looking at some other examples of runabout velocities:
"Vortex"[DSN1] . . . Sisko makes first contact with the Rakhari in the Gamma Quadrant. In orbit of the world in a runabout, Sisko is asked to return a Rakhari citizen to the planet without delay. He informs the Rakhari that they should "expect him to return in a vessel just like this one within 52 hours". In "Emissary"[DSN1], upon emerging from the newly-discovered wormhole, Dax reports that the closest star system is "just under five light-years away." The computer identifies this star system as Idran, and per Dax it is an uninteresting place . . . no M-Class planets. Even if we assume that Sisko could somehow communicate with the station and order a runabout to depart immediately, this still requires a trip of at least five light-years within 52 hours. That's just under 0.1 light-years per hour, or 842c. Of course, what actually happened is that Sisko returned to DS9 and, in his office, ordered Odo to escort the Rakhari to his world in a runabout. So instead of the unrealistic one-way trip, we're actually talking about a 52 hour round-trip. That requires a ship capable of only warp five to make just under .2 ly/hr, or 1684c.
"Whispers"[DSN2] . . . A faux-O'Brien takes a runabout through the wormhole, then sets course for the Parada system in the Gamma Quadrant. He orders maximum warp, then asks the computer for the ETA. "One hour, fourteen minutes" the computer reports. In "Emissary"[DSN1], upon emerging from the newly-discovered wormhole, Dax reports that the closest star system is "just under five light-years away." The computer identifies this star system as Idran, and per Dax it is an uninteresting place . . . no M-Class planets. So, this is at least five light-years within 74 minutes. That's a warp five ship making 4.054 ly/hr, 97.3 ly/day, or 35,513c.
For our purposes we're going to ignore that last example, since it's outside the usual ballpark of warp five velocity. Numerous examples from Enterprise (as mentioned here and here) show that warp five is usually in the 1500c range, a value in keeping with "Vortex".
Now just for kicks:
So if we were to take the 47 days and assume a speed of 1500c, we would get a range of 193 light-years for the runabout. On the other hand, if we assume 47 days and 100c, then the range is 12.9 light-years.
These are neither upper nor lower limits, nor even valid numbers ... it is only a possibility. After all, we do not know the velocity of the runabout, and hence cannot know details of the fuel consumption rate. And again, we don't know how much fuel the vessel had aboard to start with.
To put it another way, if I run an engine at 1000 RPM with a quarter tank of fuel I might go 100 miles. If I run the same engine at 4000 RPM I might not make it as far, though I be going somewhat faster.
Alas, we can't know everything.