Do I have a shot at a top university?

I have been doing a great deal of college research and most of my favorite universities are quite selective and there are a couple Ivy Leagues on my list too.

Now I know that these colleges take the best of the best, but I wanted to know if I have a shot.
I have a 4.0 unweighted GPA, am a student leader of a music performance organization that is not a part of my school, I have leads for multiple years in our school musical, do area-all State, and all county, jazz band, pep band, and French club.
Furthermore, I have 3 years of varsity sports (I know I don’t want to do them in college, but I figure I’d mention them), have 10 years of piano lessons, almost 5 of Vocal lessons, have placed in Vocal competions, and am about to be inducted into NHS.
I’m predicted to be 4th (possibly higher) in my class, take my AP histories, I’m a year ahead in science and math, have honors English and plan to have an all AP schedule next year.
I also give piano lessons and have a blog. With the exception of the blog and pep band (which is new this year) I have participated in everything for all 3 years of high school.
However, I don’t have a very good SAT score. My highest complete SAT score is a 1350, but my highest superscored is a 1390 (710 in Reading/Writing and 680 in math). I’m planning on taking the SAT one more time, as I am a junior, but I don’t have hope for a huge jump.

Do I have a shot at Cornell or even UPenn? I’m also interested in Boston University and Boston College, and I really like Northeastern too. Should I put all my effort into the SAT practice and would it give me a better shot?

I’m interested in a communication major and a music or musical theater minor

Raise that SAT to a 1500+ and you should be fine.

Your class ranks and extracurriculars are plentiful for any colleges I would say. You do have an excellent GPA but the try to get your SAT score up to at least 1450. SAT score is not all they look for so if your other things, like essays and extra activities are good, then you have a good chance to get into top-notch universities.
Your AP courses also proved that you take rigorous courses, so that’s a plus.

I think you’ll have a shot!

You may want to try a practice ACT – I have a kid making straight A’s in calculus who also struggled to pass 700 on SAT math. She got a 36 on ACT math with little math studying. She needed some strategies for finishing reading on time and getting used to the science section, but only reviewing mistakes on practice tests for the math.