A silly nitpick:
To be sure, Data was saying that getting the message across the 2,700,000 ly would take "fifty-one years, ten months, nine weeks, sixteen days-" before being cut off. That doesn't sound like the sum total of 51 years, 10 months, 9 weeks and 16 days, because 9 weeks is more than a month, and 16 days is more than a week! Nobody would say "I'll be there in one week and sixteen days"...Subspace message between galaxies was at 142 light years per day.
Actually, it might make sense for Data to say it that way since he is suppose to be "quirky" in his manner of speech. When you watch the episode, the context is certainly the sum total of the time for the message to reach back. Nobody, except Data, would say it that way
Assuming the section of map where this travel plan was demonstrated wasn't zoomed in against the general background of the galactic disk... Which would be a fairly workable way of eliminating this outlier datapoint."Between star systems" seems to suggest some fairly fast speeds crossing a third of the galaxy in weeks according to "The Chase".
It could be interpreted that way, although when you watch the scene it looked more obvious that he was thinking of zipping around parts of the galaxy.
http://tng.trekcore.com/gallery/albums/s6/6x20/thechase067.jpg
On the other hand, we do know that there was an intentional shift in the TNG production to "slow things down" so that between star system travel would be slower than how it was in TOS. So for TNG, it could be argued that between system travel was probably much closer to between galaxy travel speeds.
@Black_Dranzer - thanks for the datapoint. That would mean W9.9 = roughly 58 ly / day in the Voyager series. I found another one in "Maneuvers" where Kim mentions "2 billion km/s" but no warp speed. That's roughly 18 ly / day. Even at 18 ly / day, that would translate into only a 10 year return trip vs the 70+ year quoted in "Caretaker".
You also have to distinguish maximum speed (emergency speed) from maximum safe cruising speed. That could account for the discrepancy.