If I don't get an internship, how can I best use my summer to position myself for my academic and work objectives?

This is a difficult question to answer without knowing what your academic and work objectives are. Frankly, in this situation I would counsel you to enjoy what is likely to be your last summer without professional employment. Something to consider is a summer (or partial summer) abroad program.

Many law schools offer academic programs abroad during the summer. I spent half my first summer after law school in Rome studying international law. I never intended to practice international law but I got to spend 8 weeks in Europe, I got academic credit, and I got some great stories to tell at job interviews when I got home. (Since finishing law school, I have never taken more than a week away from work and I have never made it back to Europe!) Enjoy this time.