The filing fees for bankruptcy are the same in every state, including Ohio: $335 to file under Chapter 7, and $310 to file under Chapter 13.
If you hire an attorney, you'll have to pay attorney fees as well. How much an attorney will charge depends on which Chapter you file under and how complicated your case is. Attorneys typically charge more to handle Chapter 13 cases, which are more complex. Attorneys also charge more for cases that require them to handle special issues. For example, if you want the attorney to file a motion to try to discharge your student loan debt (which you usually can't discharge in bankruptcy) or a creditor argues that its claim shouldn't be discharged because you engaged in fraud, the attorney will have to spend more time on your case (and will charge accordingly.
If your case is relatively straightforward, an attorney might quote you a flat fee. In other cases, an attorney might charge by the hour. Before you hire a lawyer, find out how he or she charges and get an estimate of your total bill for the case.