Infantry – I agree with Brock.  Don’t get too wrapped up in the “extracurricular activities,” but don’t avoid them either.  We have an enormous Army, but a very small, tight community of Officers.  You are going to serve alongside these Officers throughout your career and BOLC is the perfect time to begin building relationships.  I also agree that you should spend some time at historical sites – an excellent suggestion.
Also, this seems obvious, but I guess worth saying…study, rehearse, form study-groups, exercise like your life depends on it (it might one day), build relationships, stay out of trouble, no drink on Earth is worth your career if you are planning to drive, don’t cheat (see studying), ask questions, learn your field craft, be a gentleman/lady, lead from the front/by example, be bold/take chances, and, yes, have fun.