Listen to "Bob." (
) He knows what's he's talking about.
I will add that I probably wouldn't app to Y with a 3.1-3.2 unless you get 168 or above. Of course you never know what could happen, but unless you have $70 you don't mind dropping on a dream or there's something absolutely, indescribably amazing in your background that you haven't shared, I wouldn't spend the time writing the 250.
I'm not trying to be discouraging. I think that with great packaging, a strong, non-whiny addendum on the GPA, and an LSAT of 165+, you have a shot at H and S and certainly Penn. Even with something slightly lower than 165 you may have a chance with Penn. Make sure you either get your app in very early or write the add'l essays: Penn had a bizarre admissions cycle this past year and there's really no telling what will happen this time around, esp. if their early app numbers are up again. Maybe you should apply to Penn Early Action so they know you're serious about them.
Why Penn, other than the fact that it's in the fam? I'm curious, and answering this question will also give you a jumpstart on one of their optionals.