Like the format of entry two, and how the "DHM" and isolated - maybe make these first letters bold? Other thoughts: When you first look at the tree icon, it looks like a brain in shape - can you modify the tree slightly or add color to the leaves possibly?
I kind of liked where you were going with this...Can you make a block behind the rest of the letters/name of hospital, make the font a little more interesting, and make a two-color logo (like blue and green or put a splash of teal with a navy background?)