Looking at the Empire in 1071 I think that had Manzikert gone differently - maybe enough to ward off the Turkish entry into Anatolia - then the Empire has to prioritize. First there need to be internal reforms and shoring up both for the government and treasury. Romanos has to defeat the Duokas Family and hold on to Anatolia. The civil war following Manzikert seems to have been the real crux in the fall of Anatolia, so avoiding that is going to be the key. With Romanos alive and Michael VII still in place to take the throne, the stability of the Empire can be maintained. Maybe it could be arranged for Michael VII to retire as he did in OTL and still get Alexius I to the throne, but either way there *has* to be an effective government in Constantinople otherwise little changes. A stable government holding onto Anatolia, Armenia, and the Balkans will look at a few key territories first -
(a) Southern Italy/Sicily
(b) the Levant/Holy Lands
(c) Caucasus Mountains - Georgia, Azerbaijan, Dagestan
(d) Upper Balkans/Venice
(e) less likely Wallachia
(f) less likely modern Tunisia
That is also likely the order they will look to for conquest. If the Byzantines can retake the first two then Egypt will be targeted. I could see the Byzantines taking Venice and southern Italy then trying to move for the eastern Papal States to connect their territory by land, if this occurs reunification of Italy will be a strategic goal.
Most likely I think *if* you avoid Manzikert and get a stable pair or triad of strong emperors then they retake southern Italy/Sicily, Tunisia as it is Norman at the time, the Caucasus region where they already had loyalties and signifciant headway, and the Holy Land (the latter some time following the death of Alp Arslan in 1072). The upper Balkans would be within reach, as would Egypt, though I think Venice and Alexandria will remain Byzantine only in the dreams of those Emperors. This does not guarantee the stability or premanency of the conquests they actually do take. Waiting until 1084 when Venice gets its fleet smashed against the Normans would allow Byzantium to try to exert control over both, and if Venice is to become Byzantine that is the singular best chance. Egypt is still under firm command of the Ayyubid dynasty and Byzantine control here would require luck and skill.
The bigger question is what happens to the rest of Europe if Bzyantium wins at Manzikert. With a stable Empire eyeing or taking the Holy Land there is no First Crusade. With no First Crusade many of the seeds for Europe's revivial in the 12th century, the trade links that revitalize the economy, and the removal of so many warlords and their progeny do not occur. Europe will likely see more internacine warfare. More interestingly it will lead to a problem in the Papal States as Urban II has to contend with several opponents and can not rally the Crusade as proof that Christendom follows him. I doubt he turns to Constantinople for help, but if the Empire is still powerful and perhaps expanding in 1090, who knows.