Heidegger's Bible Handbook: 2 Timothy: Place of Writing

3. It was written at Rome.

It is undoubted that this Epistle was written at Rome in bonds. For he describes himself as a δέσμιον/prisoner/bound, 2 Timothy 1:8; 2:9, and even implies that he was ἐν Ῥώμη, at Rome, 2 Timothy 1:7, and delivered ἐκ στόματος λέοντος, from the mouth of the lion, namely, Nero, 2 Timothy 4:17; and he indicates what the future would be concerning himself, namely, that he would be poured out, and delivered from every evil work, and preserved unto the heavenly Kingdom, 2 Timothy 4:6, 17, that is, implying that his suffering was at hand. Now, that he endured suffering at Rome, on the very day on which Nero died, the constant tradition of the ancients holds.