Chance me for some top universities?

<p>Hey guys,
I've made a pretty solid list of colleges that I'd love to go to, but I'm having trouble gauging where I stand. I'm thinking of double majoring in Engineering (mechanical maybe?) and Economics (or some other form of business). </p>

<p>Schools I'm looking at (in order of interest):</p>

<p>Dartmouth (1st choice)
Yale
UPenn
Middlebury
Duke
Northwestern
Boston College
University of Chicago
Amherst
University of Illinois - Urbana Champaign
University of Southern California</p>

<p>State: CT
School Type: fairly competitive public
Ethnicity: Asian
Gender: Male
Hooks: legacies (grandparents) at Columbia and UPenn</p>

<p>SAT I - 2050 (700M, 680W, 670CR) I'm retaking in the fall, along with the ACT for the first time.
SAT IIs - taking Math II and Physics this Saturday...I took chem last year without studying and did pretty badly (680)
APs - I took Spanish Language and Lit last month...probably 4s in both.
GPA - ~3.82
Class Rank: top 20/400+ I'd say? something around there
Senior course load - AP physics, honors human anatomy, AP Calc BC, AP stats, AP psych, honors world literature, honors modern poetry.</p>

<p>Extracurriculars:
- top 16 award swimmer for 5 consecutive years, placed 2nd at state championships (26ish hrs a week) --> I'm going for recruitment at NESCAC schools and attempting it at some ivys
- piano: winner of a state piano competition, honorable mention in 2 other separate piano competitions, 3rd place in another state competition, winner of a contemporary piece competition, soloist at school, benefit concerts (6-7 hrs a week)
- violin: member of an audition-only regional orchestra for 3 years, member for an audition-only state orchestra for 2 years, participated in the CT high school music theater award-winning pit orchestra from Les Miserables, principal 1st violin in school orchestra <a href="6-7%20hrs%20a%20week">2nd seat</a>
- Founder and president of Odyssey of the Mind [an international creative thinking club, we do mostly engineering projects. Our team won 4th place at the state competition this year]
- Co-president of Freethinkers club [philosophy, culture, politics, basically a discussion club for any and everything]
- Co-president/reviver of Future Business Leaders of America
- Composer
- Photoshop artist, graphic designer
- I plan on sending recordings of my original compositions as well as of my senior recital (for piano and violin)
- Winner of Excellence in Music award and Society of Women Engineers award for excellence in natural sciences and mathematics at school (I'm not sure these matter, but they might)
- 250+ hours community service at a nursing home, I plan on finding a place to volunteer this summer that has to do with engineering or business
- Getting a job this summer</p>

<p>Recommendations should be excellent from both teachers and swim coach (whom I plan on getting an additional rec from). Peer evaluation (for Dartmouth) should be awesome as well. Not too sure about my counselor, but it should be at least decent.</p>

<p>Might look at a school like Holy Cross foe economics as HC has very good alumni network in the business community.</p>