I've always had a doodling problem as far back as I can remember. Even when there's a meeting and there's a notepad in front of me, you bet I'm doodling. You guys might draw blueprints to your dream homes, dream girls, and golf courses but for me, I've always liked designing stadiums. It's not that I had an obsession with the intention of becoming an architect, but I'm fascinated with architecture, baseball stadiums especially. Back when I was in high school and college, I'd draw my own manga on the side while I took notes in class. Oddly, drawing in class and during staff meetings actually made me concentrate better.
Especially if you're working in accounting/finance or any job that requires number crunching, bring a graphing calculator with some TI games built in (at least that's how I got through high school). Might be a bit noisy pressing all those buttons but it's not too distracting where you rub your fellow co-workers the wrong way that you're unprofessional. Of course, if you use a computer on the job (albeit no Internet), there shouldn't be too much problem in staving off boredom. For example, you can teach yourself advanced Excel functions.
I don't have any other suggestions that you haven't heard here, but if I were you, I'd ask your supervisor if there's anything you can help in. It's one thing to ask him/her to give you more work, but another to ask what tasks you could help around in. Could score you some kudos points with your employer. It's also the kiss-arse way of doing things (which deep down inside I don't personally advise), but given that you're relatively new in the working world, it could get you off on the right foot.