On foot
Walking around the OSU area is more than common, many walkways exist try to avoid alleys after dark, and the locals are very patient with those crossing streets. There are some homeless and beggars like most metro areas, but the best way to deal with them is by ignoring them or just a stern NO and move on, if they ask for money, which is uncommon. All in all, walking in the OSU area should be considered safe and enjoyable.
By bus
The COTA bus service (http://cota.com), while not by any standard one of the greatest in the nation, can take you to most important places in the city, which should be about 5 blocks away from any conceivable location you need to go to. This service costs $2.00 for an express bus and $1.50 for a normal bus. Transfers are free; ask for one from the bus driver when you pay your fare.