There's plenty to do while on OJT/OJE (being stuck on it myself):
OPME, Second Language Training, Air Force Officer Development - You'll have to do these eventually anyway, so get them done while you've got free time. OPME and AFOD are offered DL, and you can often work on them during work hours. I don't have links off hand, but OPME is done through RMC, and AFOD is through CFSAS (17 Wing).
If you get the chance, there are other qualifications you can usually get locally - Presiding Officer, Harassment Advisor, etc. that come up every now and again. You might be put on the bottom of the list as a 2Lt, but by no means does that mean you won't get on the courses. These staff qualifications are good to have.
Take a look at your Wing's Ground Training unit, they should offer courses every now and again that can kill time. Don't forget about your IBTS either. Talk to your unit training coordinator, as the full IBTS set (FA, C7, 9mm, Nav/Comm) can easily occupy about 2 weeks.
Heck, if you're feeling lucky, there's residential courses you can try your hand at. Off the top of my head, there's Radiation Safety Officer, General Safety Officer, Basic Parachutist, and lots more. Look up various schools on the DWAN and see what's out there.
There's nothing stopping you from doing these on your own time and dime. You might be able to go to RMC for a Masters in Military Studies (or whatever it's called), but don't count on it if you already have obligatory service. If you're doing some courses via DL, your supervisor may allow you to study during work hours if you have nothing else to do, but don't sign up for a course counting on that.
Take advantage of small taskings that come up. Usually there's lots of staff work that needs to get done, which while mundane, is at least something to do. I'd wager someone, somewhere in your building is behind on filing, or needs a filing cabinet reorganized.
Put your talents to use. You'd be amazed what skills are in demand at various places. Depending on your education and/or interests, you might be able to get assigned to another section/unit to put said talents to use. Getting such a job can be incredibly rewarding, especially if you achieve something concrete for the unit.
If all else fails, study the regulations and relevant publications. A good knowledge of those is essential if/when you become a supervisor.
Find yourself a hobby or project for after hours. Going from the office to playing video games in the shacks every day of the week gets old real fast. Get involved in the community both on-base and off-base, there's got to be at least a few clubs one can take an interest in. If not, feel free to form a club and put your leadership skills to use.