I've been there waiting for 67 in the wee hours about a dozen times, and the scariest thing that's ever happened was the time I nodded off briefly and was woken up by a guy I went to college with years ago (also waiting for a train). I wouldn't worry about it. If you have plans that keep you out on the town until 1 or 2 am, it's nicer than waiting in the station itself, but here's the routine I typically follow.
If I'm in the station early enough, I'll stop by Tracks, a bar/restaurant on the LIRR level outside the 7th Avenue Subway (123 trains) entrance. It closes at midnight or 1, I forget, but it's a good place to kill time. Some of the smaller delis, etc. in the station will also be open quite late, possibly even until train time, but these are all take out.
I then walk over to the waiting room and show my ticket. There's usually a couple dozen people at least, some waiting for NJT trains, some with bad connections (traveling south from the Maple Leaf, for example). Before the last NJT trains leave, around 1:30, Amtrak Police do a ticket sweep and escort out anyone without a valid ticket. I typically fight to stay awake, but it's hard to sleep (lots of prerecorded announcements) and I wouldn't recommend it.
I check the monitors to see when the trains arrive and grab the track number so I won't have to wait for an announcement later on. (It's briefly posted when the train comes in, then disappears.) I'll typically wait inside until about 30 minutes before train time, then walk over to the gate and hang out there. Boarding is typically 20 minutes before departure even though the train may be sitting in NYP a while.
There will be other people around--cleaning staff, and on a weekend, drunk suburban college kids--but the waiting room feels safest, especially after the sweep.
I've also done late nights at WAS and LAX (waiting for the 1:30 am bus to Bakersfield) and NYP felt the most secure because the waiting room is always staffed, police were frequently seen, and there were definitely other travelers; LAX felt a little uncomfortable. (Then again, I was a longtime NYC resident...)