Yes, Emperor Justinian attempted to reconquer the west. After making what was optimistically called an "Eternal Peace" with Persia, Justinian and his key generals Belisarius and Narses conquered the Vandal Kingdom (a Germanic kingdom ruling Tunisia, which then was simply called Africa province), the Ostrogothic Kingdom (a Germanic kingdom ruling Italy and Croatia), and parts of the Visigothic Kingdom (yet another Germanic Kingdom ruling Spain and southern France after the fall of the Western Empire). The Gothic War in Italy lasted almost 20 years, and was very costly for the Empire. Justinian's empire was also weakened economically by a great plague during his reign, preventing him from pushing further into Spain or attempting to reconquer any parts of France. However, by Justinian's death, Italy, Africa (that is, Tunisia and Algeria and Morocco), and the southern coast of Spain had been recaptured.

Rome itself had shrunk greatly due to its decline starting in the 5th century and Germanic rule, but the Gothic War impoverished it and much of Italy even further. As such, many of the western territories were not as profitable for the Empire as they were for the united Roman Empire of centuries prior. Also, the city of Rome didn't really become a major center under Byzantine rule, but rather the city of Ravenna become one of the cores of Greek/Roman control in Italy, as it had been during the Western Empire and Ostrogothic Kingdom.