I am a Brooklyn resident, and I have applied there. Crossing my fingers.
The area in which the school is located is in the Downtown area of Brooklyn. You can find a lot of information at
http://en.wikipedia.org/wiki/Downtown_Brooklyn
To clue you in on the area's safety. I would general say it is pretty safe. With all the hussle and bussle of daily business going on in the day, there is an assured feeling that the many pedestrians are always walking by. Most of which are professional business men and women, law students, fellow LIU students, court officials and government offices that employ many government employees. So during the day, i would say it is very safe.
The entire area is full of government buildings, two very large shopping centers, the Fulton Street Mall, and the Atlantic Center shopping center which are only blocks from each other. There's the Broooklyn Academy of Music and theater, where many of the cultural aspects come into this area.
Not to far from the LIU campus is the Brooklyn central library, Brooklyn museum, Prospect Park, and the Botanic gardens.
Also one of NYC's second largest train hubs is located right on the LIU campus.
The entire downtown Brooklyn has transformed over the years and the image of NYC being unfriendly has changed. But of course where there's many people, they wont be obliged to make friends with strangers.
The areas of concern in Brooklyn is ususally the residential areas, mainly the projects which are a few neighborhoods away in Bedford-sty and Bushwick area.
Keep in mind, there are always bad people that go out of their neighborhoods no matter where you are and make trouble elsewhere, so do keep an open eye for shady looking people if you take late night classes.
As for St. Johns, i believe it is in a residential middle class Queens area. It's culturally diverse and you can see Asians, Latino predominantly walking the streets there. I've never really been there, but have passed through in a car. I cannot assure you that it is safe there, because there are always bad people out there, it's just if you are in the wrong place at the wrong time.
http://en.wikipedia.org/wiki/St._John%27s_University_(NY)