It's curious that so many people go for the arms. I wonder why.
Upper arms, belly, chest, thighs are probably the easiest places. Won't hit anything vital. There is no rule saying you can't go over old scars. I have scars that cross.
Technically you don't have to cut at all unless you just really have a thing for bleeding.
I have cigarette burns along my wrists but there's burning/branding in general.
There are more sophisticated and discreet methods as well.
You can just exercise. Literally no one will bat and eye and you're still putting your body through hell. Martial arts conditioning is really good, any extreme routine will do the trick, or even something as simple as planking on your knuckles.
You can squeeze ice.
You can self flagellate. This one is even done by monks and certain religious practitioners. You may even discover a new kink.
You can walk around on your knees.
Pull your hair out. No one will notice a few strands, but you can just do your body hair instead and not worry about that at all.
Honestly, the list of ways to casually hurt yourself for masochistic reasons is so long that the easier question would be how not to do it.
I personally wouldn't recommend any of it but if your brain got wired wrong when you were developing and pain got tied up in your pleasure center like me then who am I to stop you.