I'm not aware of any extended time he spent in Rome after being elevated. He made several trips there for various ceremonies and events.

The only thing that is leaping out at me is that it was possible that he spent some time in and around Rome during the Postumus rebellion, however Postumus never actually invaded mainland Italy or directly tried to unseat Gallienus. Without those threats, it was likely he just stayed out in Gaul and the Rhine campaining

Gallienus did spend time in Illyricum, however, and that's likely as close as you're going to get during the end of his career.