You are very right. Keys are very useful too, or even the edge of your credit card to slash someone's face. Other tool is normal pen or proepr self defense (you can get one from ebay).
True about elbows. Also when someone tries to grab or choke you from behind, you can just hammer punch or hit them with open hand to the groin repeatedly, or stomp on their toes with all the power using your shoes (very painful). Kicking their shin with back of your heel is good too, especially if they try to lift you (just have to remember to wrap the other leg around their leg so they cannot lift your properly).