I too have felt bad discarding a car that I know someone could have used, but didn't know how to find them. I have driven a few cars to the scrap yard! You need to realistically assess the cars safety. I have driven many an old car that was safe for me, because I was aware of the quirks...but what if you give or sell it to someone else? Will they be able to work around any issues? This always makes me think of the experience of loaning someone an old car. If it takes so long to explain to them how to drive it and what not to do, they shouldn't be driving it! I had an old diesel that lost its shut off solenoid, so to shut it you had to either leave it in gear with brake on and let out clutch to stall it or stuff a bag into the air intake. That same car also had a bad starter that only worked once in the while. Conveniently I lived and worked places where I could park on a small hill to give it a roll start. That car worked like that for a long time for me, but it wasn't for everyone!
If it really is a car that anyone could get in and be safe, Craig's List would be my start point. If you really don't want anything for it, and just want to give it a good home, you can even list it in the "free" section.
Good Luck