What to Do to Improve Chances

I am currently a High School student finishing up my Sophomore year - I have a 3.85 unweighted GPA and a 4.1 weighted GPA. My school does not do official rankings until the end of Junior year, but I know I am at least somewhere in the top 15% of my class. I am from New Hampshire, and attend a public school of less than 500 kids I hope to go to Cornell, UNC-CH, or Johns Hopkins.

I plan to take every AP class at my school through my Junior and Senior years (of which there are 7, none open to Freshmen or Sophomores) as well as another AP course online. 12 Honors Courses so far.
I am yet to take the SATs, the ACT, or the PSATs.

ECs:
President of Tri-M
President of the Math Team
Founder and President of the Politics and Economics Club
2 time Youth + Government Delegate with intention to go again
Francis Wayland Parker Scholar of the Month (One of 8 students in the state for 2016)
School Level Awards
Science Club Member
Tutor
Hospital Volunteer
Attending Future Leaders Institute at UNH this summer.

What can I do during my Junior and Senior years to improve my chances towards a school like Cornell?

Keep doing what you are doing. Do well on your standardized test – prep and leave time to take twice. If any of your schools require or recommissioning subject tests, also study and leave time for a retake. If you can extend any of your activities or award beyond the school level, do that. Run the net price calculators on each college website with your parents to make sure they are affordable. Develop a solid list of matches & safeties, as those are all reach schools.