One summer I worked at a Girl Scout camp. The most important lesson I learned there was to keep a first-aid kit handy. I have them all over the place: in my linen closet, in my car, and in the box I take to the local pool and keep there all summer. But the most-used kit I have is in the kitchen. It takes up hardly any space, and it's in the place where many accidents happen.
I put a small tube of Neosporin in a box of assorted band-aids, and keep it in a cabinet. That takes care of most quick bandaging needs!