Ohio State isn't too bad, at least the campus area isn't. There are a lot of people on bikes, though most of them don't follow traffic laws very well - and nicer bikes can get stolen if locked up on campus inadequately, though the campus police offer(ed?) a registration program for student bikes.

Off-campus, Columbus is not at all cycle friendly unless you live in a neighborhood like Clintonville. There are a lot of big, multi-lane roads with fast/aggressive drivers on them. The smaller roads don't often have much of a shoulder to avoid traffic, either.

Basically, the bicycle commuter options for Columbus really vary in relation to where you will be living/shopping and what your comfort level with traffic is. Ohio traffic laws do not actually deny cyclists the sidewalk (as far as I understood from my last reading of them), so that IS an option if things get hairy.