Definitely perfect your typing skills. Read a lot, including some boring *&^%, just for practice. Go to a law school section in a bookstore (law SCHOOL section, not real law stuff) and just get familiar with all the supplements and study aids. After that, it depends on your major.
If you majored in pre-law or you've been around lawyers your entire life, relax and hit keg parties all summer.
I majored in philosophy and minored in English. I'm not sure when all that "deep thinking" is supposed to come in handy.... Law school readings (mostly cases) can be long and hard and boring, but once the rules are sifted out, it's all memorization. Compared to people who majored in areas like accounting and math, I need MEMORIZATION skills--which require a high tolerance for repetition, something I lack. This summer, I will work on memorization!
At my school, the impact of writing skills is minimal the first year--one 3-hour class first semester, and I now know that legal writing breaks most of the rules of "good" writing in other academic fields.
So...if I were doing it all over, I would work on memorization and read something like Law School Without Fear. Twice. Maybe once in July and once in August.
I would also watch Law and Order often. Seriously. It'll give you a context for your criminal law class.