Time to live up to my reputation as THE Ohio State University troll...
After Ohio, the #1 destination of tOSU Moritz grads the past few years has been Washington D.C. OSU has strong ties to D.C. due largely to their Washington D.C. summer program (for UC kids, think 'UCDC' but for law students). Check it out and see if it interests you. Students I talked to highly recommended either this one or the Oxford program:http://moritzlaw.osu.edu/programs/washington/index.php
For Ohio, Chicago and D.C. OSU places very well. Recently the placement in NYC and California has gotten a lot better too (echoing the huge rise in the US News rankings over the past decade). It's reputation as a regional school is largely based on self-selection (60% of the students are from Ohio, and 60% work in Ohio after graduation. Chances are it's the same people). Also, OSU has a strong alumni base (like most schools with big time sports programs) so when you find an OSU alum on a firm website, they are more likely to be helpful in your job search than alums from other schools (every OSU alum I've emailed has responded with very long insightful emails about their law school experience and job search).
Going to Georgetown or GW would obviously make getting a job in DC easier, but chances are you will enjoy your OSU experience more (as THE Ohio State University troll, I must make it sound like the most fun place in the world... although it seemed to be the most fun law school I visited).