The Botany Bay if limited to sublight engines could've accelerated up to a moderate percent of light speed and by the time the Enterprise found them traveled 100 or more odd light years away from Earth.
Amusingly, if you assume the ship could do 0.45 times lightspeed, the relativistic math would make the time differential between 1996 and "Space Seed" match Kirk's vague statement that 200 years had passed. For Khan, two centuries (that is, less than 250 years) would then have passed, even though the difference between 1996 and 2260-whatever is greater for Kirk.
That would indeed place the ship a bit more than a hundred lightyears from Earth - well matching the given facts of this being a region where Earthlings previously traveled but later abandoned, presumably because they moved on to more distant pursuits. And a hundred lightyears from Earth is just about believable for ST2:TWoK as well, for a location that Kirk could visit on his pleasure cruise, a location where Starfleet would hide a secret research facility, a location where two starships meeting would be unlikely, and so forth. It would even be well within the abilities of the ENT-era Earth to utilize as a final desperate hideout, "Twilight" style.
(Incidentally, it would also allow Ceti Alpha to be a star in the not-so-distant-on-the-average constellation Cetus, and thus conform to standard stellar naming: it might be something like Gamma Ceti A, shortened much like our heroes shorten basically all of their stellar names.)