Summer of Junior Year

I am currently a junior and I am looking to apply to some of the top universities in the country. I am going through the process to apply to my state’s Governor’s Honor Program and I am wondering if that is a good way to spend most of my time in my final summer before applying to colleges. Would it be better to apply to an internship or something similar to that in a hospital or go to GHP for mathematics? Both sound like excellent ways to go about my summer, but I am not sure if one is more rigorous or looks better on a college application.