If I have unsold inventory in my small business and want to donate it and deduct it as a Charitable contribution, where would I put that on my Schedule C?

To reduce your inventory for the donation, indicate that the donated inventory was "removed for personal use". Then you can indicate your "personal donation" under the Deductions and Credits tab in the Charitable Donations section. See the info below on how to value your donation.

IRS Pub 334 Donation of inventory. 

If you contribute inventory (property that you sell in the course of your business), the amount you can claim as a contribution deduction is the smaller of its fair market value on the day you contributed it or its basis. The basis of donated inventory is any cost incurred for the inventory in an earlier year that you would otherwise include in your opening inventory for the year of the contribution. You must remove the amount of your contribution deduction from your opening inventory. It is not part of the cost of goods sold.