After the permanent division of the empire by Theodosius I (379-395), only he (from the east) and Valentinian III (emperor of the west from 425-455) visited the other half of the empire. Theodosius did so twice to impose his authority on the west, first to defeat the usurper Magnus Maximus and restore Valentinian II, and the second time to defeat another usurper called Eugenius. I guess Valentinian II also counts, since he fled to Theodosius to ask for his help after being kicked out of Italy by Magnus Maximus. Valentinian III, Theodosius I's grandson, was partially raised in Constantinople and then moved to Italy after his uncle Honorius died - in 437, Valentinian III returned to the east to marry Licinia Eudoxia, daughter of Theodosius II. This was I believe the last time a recognised western emperor visited another imperial capital.

Technically, as a few western emperors, such as Honorius, Anthemius and Julius Nepos, were imposed by the east, I guess they could also count as 'eastern' emperors 'visiting' the west too. After Theodosius, the next proper eastern emperor to visit Italy would be Constans II, Eastern Roman/Byzantine Emperor from 641 to 668, who moved to Italy in the 660s to secure his western territories - he even died in Sicily, as he was murdered there by a servant whilst having a bath (allegedly with a bucket).