Speaking as someone who lived in Bayonne for 18 years, and who continued to visit relatives in the city for many years thereafter, I can tell you that Bayonne as a whole is a safe town.
Is Bayonne pretty?
Except for a few select neighborhoods, no it is not pretty.
Is there nightlife?
For most people, the answer would be no.
However, for an urban area very close to NYC, it is safe.
In fact, there are several areas of Jersey City that are distinctly
unsafe, unlike Bayonne, where there are no really unsafe areas. Some areas of Bayonne are...not particularly desirable...but they are not an urban jungle.
As to the neighborhood that you mentioned, I would classify it as an up & coming area, due to the opening of the decidedly upscale
Silk Loft apartments located right in the area that you are considering.
(Hmmm...Actually, you might be talking about this development, even if you didn't mention it by name...)
The neighborhood has traditionally been a somewhat gritty lower-middle class area, consisting of 2 family wooden homes, built about 100 years ago--with varying degrees of preservation, plus some commercial buildings that are...old and unattractive. However, now that young professionals will be moving into that Silk Loft adaptive re-use development, the area will be dragged upward, and I wouldn't be at all surprised to see more adaptive re-use taking place in that area.
Additionally, you would be only a 5 block walk from the Light Rail station at 22nd St, thus giving you easy access to mass transit into NYC.
In case you are not already aware of the Silk Loft development, here is a link:
Hoboken, NJ Apartments | SilkLofts
(Despite the wording in the link, these apartments are NOT in Hoboken!)