A few fun facts. There are indeed dozens (36, apparently) of dwarf galaxies that are closer to the Milky Way than Andromeda. Of those, 15 orbit Andromeda, 20 orbit the Milky Way and 1 orbits the Triangulum Galaxy (second closest major galaxy to the Milky Way). The smallest of these 'dwarf galaxies' seems to be about a fourth of the size of the Milky Way — so it's still pretty damn huge. The nearest dwarf galaxy is 25,000 light years away and it's about 3/4 of the size of the Milky Way. By comparison, Andromeda is slightly larger than the Milky Way but stands 2.5 million light years away.
Now, do notice I'm not an expert and all this comes from a very cursory Internet search, so don't take my word for it. But I would agree that, in practical terms, it would probably be better to send the 'Ark' to one of the dwarf galaxies close by, even if it's just temporarily. It would serve its function just as well, within the story as well as without. However, I can see why they went with Andromeda. Beyond the name recognition, going in a one way expedition to settle and explore Canis Major Dwarf doesn't sound quite as glamorous as doing the same for Andromeda, nearest major galaxy and largest in the local cluster.
Once again, form wins over function. Whether you're okay with that or not, well, that's rather subjective.
EDIT: Revision
Now, let's go with the fastest ship available to us, namely Reapers, with an astounding 30 light years per day. At this speed, it would take about 230 years to get to Andromeda, assuming no stops and a direct trajectory. Under those same conditions, it would take less than 3 years to get to Canis Major Dwarf. Which... isn't good. If our hypothetical Ark wanted to escape the Reapers for good, Canis does not seem like a very good option. Admittedly, there are others, but two or three centuries to Andromeda actually sounds pretty reasonable.