That's actually a surprisingly hard question to answer. Assuming we use the standard logarithmic scale offered in the TNG Technical Manual, then you're looking at Warp 9.5 being approximately 1800-2000 times the speed of light. In 123 days, assuming no malfunction and unlimited fuel, you could therefore travel 606 light years:
This tallies quite nicely with the Warp Speed calculations in the (unpublished) Voyager Technical Manual which refers to Warp 9.6 as being around 1900 times the speed of light
Unfortunately, nothing in life is that easy. The TNG Manual stresses that your speed is highly variable due to the interstellar medium you're traveling through, not just resistance and gravitation but also changes in subspace.
The actual values are dependent upon interstellar conditions, e.g.,
gas density, electric and magnetic fields within the different regions
of the Milky Way galaxy, and fluctuations in the subspace domain.
Starships routinely travel at multiples of c, but they suffer from
energy penalties resulting from quantum drag forces and motive power
With regard to the episode TNG : Remember Me, it's important to note that when Dr. Crusher asks the computer how far Tau Alpha C is from her present location, she's in a pocket dimension created by her own mind. There's no specific confirmation that this figure is in any way accurate.