Received unemployment in Dec. 2016 and fully repaid the amount received in Jan. 2017 as it was received in error. Am I required to report 2016's 1099G in which taxes were withheld?

Yes, you'll report the unemployment compensation you received in 2016 as well the income taxes they withheld. When you file your 2017 taxes, you'll include the repayments as an Itemized Deduction on Schedule A.