I always lodge near Termini station, and have walked to my hotel at Midnight. Absolutely safe! For one thing, anybody out at that time of night knows who you are. It's a business area and often merchants close up around 11 pm, and so should still be open when you pass by. Often shopkeepers will come out on the sidewalk when they see you.
They all have a vested interest to keep you safe and nobody will violate that trust. FYI I'm solo, female, 71, and a size 2, and I'm good in that area. If anything, anybody outside has only wanted to be reassured that I get into my hotel. For me, this watchful care continues thru my whole stay.
I do recommend traveling light, and knowing where you are going. For me that means one rolling carryon weighing no more than 15 pounds total, and a RS Euro Flight Bag holding my travel laptop, some allergy medicine, small pack of wet wipes.
You said northeast direction? That's where I go too. Note that you can walk inside Termini to Track 1 by the big green neon Farmacia sign and walk through the indoor to outdoor hallway flanking the Farmacia to that Via Marsala side of Termini. Check Google map before you leave to track your route!