Pre-learn all the material for the fall semester over the summer. Do all your shadowing, volunteering, soup kitchen, leadership, personal statement, secondaries essays. Wouldn't hurt to start on some FA and Step 1 prep, especially Anki. Finally, start emailing different neurosurgery programs to express interest.
(joke)
Seriously though? Take a vacation, go on a tourist trip, go backpacking before the semester starts so you can have a natural waking up and going to sleep time for the semester. Start reading and make it a habit which will help for CARS on the MCAT and is also just good for your own culturing.
But don't get caught up with medical stuff yet. Do things you can't do later. The only thing you should
never do is spend the whole summer lazing around. Do something active, go outside like I said, or get involved in a summer camp or program. And hey, if you really are excited to get into premeddedom, then start thinking of getting a CNA or EMT certification in order to work in a hospital setting during college. That's good too.
But... chill... from career stuff that is, go hard on the fun stuff mentioned above.