I think it is not unfair to say Justinian's borders are achievable to be held on the long term. With competent leadership and no big threat in the East, I would say Iberia can also be conquered as well as Pannonia. Perhaps even Souther France, but that is pushing it a bit, given how Pyrenees, Alps and Carpathians could provide good defensible borders in the West, which is a traditional Roman goal (natural borders). In extension, I could see them holding some important trade cities here and there (Massilia, Crimea, etc).
As for colonization: the main driver behind it is not there for the Romans, they have easy access to India and the riches of the East. Provided that they have comfortable military, scientific and industrial upper hand, they will likely want to establish trading posts in India, Indonesia, East Africa, Malaya and all the way to China. The goal being to have a firm control of seaborne trade in the Orient, so that any resurgent Persia cannot just block (and tax) the flow of goods on the Silk Road. They might not go for direct conquest as OTL European powers at first, but if strong states form in Western Europe, they will definitely want to get a piece of the pie without having to purchase everything via Constantinople. This gives them a clear motivation for Westward expeditions. Once these "Franks" or whatever find America, the Romans will also be interested, and with the control of Iberia they are in a good position to get there. However, in this case they may be in the same position as England and France OTL, being late comers, so they would probably be mostly oriented towards North America. Would fur trade be able to complement the Eastern trade somehow? Perhaps, I could see an ATL triangle of trade here, and if Byzantium has enough surplus population, North America could be a good dumping place for that, so they might get at least part of the continent, but other Europeans would be the main players here. There is also the question of the arrival of European competitors in India via alternate routes, that could prompt Constantinople to pursue a more direct colonization policy to avoid their rivals taking a India for themselves.