Yes there's a good idea in there. I would have to think about it a bit as usual. It might be a bit awkward. It would have to be clear what's what. When you click on a clinic icon the one that's selected is already the closest one you know and there is no difference between clinics of the same type (well the people there will probably be a bit different). But I do like the idea of showing the other ones.
What might be best (but a bit unclear unless you know) that if you click on an icon (for a site-type) that the list of know sites (under the mini-map to the left of the planet-information panel) only shows sites of that type in order of distance to you.