Not a foolproof plan, but avoid the buses and subways around 2:30-4pm as that's the time the school kids will be loose. I generally avoid the large groups of kids if possible. I know it's probably insanely expensive to hire those yellow buses, but enough already using the MTA to ferry the kids back. I'd like to take a train/bus ride without 50+ kids acting like they've been released from some asylum or prison. Manhattan is probably the best place to go to as far as safety in general. If it's like a subway centric trip, the southern brooklyn bmt lines are also pretty safe. The A to the rockaways is also ok, but I'd prefer to stick with the Rock Park S than venture to the Far Rock end of the line. As long as you are staying in the station (not venturing down to the streets), then I'd say for the most part you'd be fine. I haven't been on the 3 past Utica in a while and the D past 161st, so I can't comment about those lines, but imo, probably best to avoid those lines and you aren't missing out on much anyway.
To back up the in broad daylight stuff. I was walking back home in my area and was stopped by 3 guys. One of them looked like he was smoking a joint, asked me to show him my wallet. I just kept walking away. And thank god they didn't try to chase after me. I kept a steady pace and walked a few blocks away to make sure they were gone. But that point on, I'm always on full alert even in my own neighborhood. In a sense this is where those google glasses would've been great to get a pic of the scum and upload it online.