Regarding the public transit issue, during the week the 3 train runs fairly regularly (every 5-7 minutes during rush hour, every 9-12 minutes during off hours). Weekends are harder to judge as they are constantly doing work which affects all the transit lines. However, if you don't mind walking, you can head in the opposite direction to Fulton Street to catch the C train which is a good alternative.
As for the safety issue, it depends. Your experience will be determined by where you're from and what you're used to. The park across the street (Brower) can sometimes be a rough place for neigborhood kids, but my experiences have been that he element there that is "bad" tends to focus all their energy in the park on each other and not on strangers. I'm not sure that dynamic is much different than it is for kids anywhere. Several of the troublemakers were recently rounded up, so there is some hope of a quiet(er) summer.
When my kids were younger we used the park a lot more as a place for them to practice riding their bikes or playing catch. Its not somewhere my kids hang out now that they're older, but that's because the park's ammenities don't currently mesh with their interests. The Children's Museum attracts a pretty active under 10 crowd so the park is different during the days than it is at night, if that makes any sense to you.
Hope that helps.