I'm filing a tax return for my deceased father. Exactly what should I put for the address? Do I use his last address, or enter mine?

The address on a tax return is just a mailing address. Enter the address that you want the IRS to use if they send a letter or notice about your father's tax return, or if they mail a refund.

You would use your address.  The purpose of the address on the return is so the IRS can contact you in case they have any questions or to send any checks.  

Deceased Person

Death in the Family