Narrowing down school choices for a ChemE PhD?

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Hi, I just finished my junior year at a mid-tier school in the US, and I am beginning to look into chemical-materials engineering PhD programs. I'm at a bit of a loss as to what type of schools I should apply to. For reference, here are my stats:

• GPA: 3.96/4
• Research Experience: 2.5 years by the time I am finished with my undergrad
• Publications: A couple in the works right now, likely to have one published and another one (first author) being submitted by the time I start applying
• GRE: Haven't taken yet, studying for it right now
• LoR: Can likely get three good ones, one from my PI and others from two professors I know well
• I'm also an American if that matters

As I said, I am unsure of which schools I should look into. I clearly want to go to the best programs possible, but I also don't want to be the person who only applies to the top 10 schools and is crushed when I get no acceptances. Is there a "strategy" I should use when looking at schools? Should I even bother applying to schools like Berkeley and MIT? My main concern is even though I have a high GPA and decent research experience, my school isn't very well-known for engineering.

I'm sure you all understand how confusing this whole process can be, so I appreciate any advice.

Thank you.

[Neurotic_Jay]

GPA matters a lot and if your LoRs are good, you have a decent chance in getting into a good school. Top schools like MIT are like lotteries... No one knows whether they'll get in or not until the results are released. Looking into applicant profiles in previous years may help.

Edited May 10, 2017 by Neurotic_Jay