The novel Like a Toga in the Wind about a young Alexander the Alabarch has Alexander visiting the places described below. This is fiction and there is no specific historical evidence for Alexander being at any of these places in Rome EXCEPT for the Carcer prison where he was imprisoned by Emperor Gaius (Caligula) in around 39 AD.
! However many scholars, including this author, believe that it is likely that Alexander spent some time in Rome where he became friends with Claudius. If so, then it is very plausible -- even likely -- that the real life Alexander did visit many of the places described below.