It really depends.
In brooklyn, you might wanna consider to stay in park slope, blooklyn heights where very closed to or immediate to the city; however, I stongly not recommend to stay far from the city since brooklyn is getting worse in terms of safety. In queens, Astoria and sunnyside would be a good shot. Usually queens is cosidered to be safer place to live.

recommand Rego park, and Forest hills.
It is safe. and transportation is nice and close to flusing.
When I find apartment, I considered express subway. And if there is station in town, I checked if the town is safe or not.
Forest Hills is little bit higher than other towns in Queens because of good public education as residents say.
Rego park is also nice close to forest hills
But I decide to live in New Jersey.
I do not know which is safe or not. If it is race for example, black, hispanic, I recommand you to look at the school statistics.
It is helpful.
Good luck