The first season of The Lord of the Rings: Rings Of Power ended with a fiery bang, not only the one that covered Morder in ash but also the revelation that Halbrand was Sauron. According to the lore and history of Middle-earth, Sauron wandered through several kingdoms during his exile from Mordor after the War Of Wrath, often appearing in a more pleasing guise to fool the locals into helping him with yet another nefarious plan. Lord of the Rings: Rings of Power seems to have adopted this idea, with his influence on Lindon and Numenor already evident.
One doesn't just walk into Mordor unless they're the Dark Lord himself, and last we saw the character formerly known as Halbrand he seemed to be doing just that. Other than returning to the place that he and Morgoth built, what other travels does he have in mind?
7 Barad-dûr
The infamous tower that was crowned with the lidless eye in the Peter Jackson movies was a place called Barad-dûr, also known as the Dark Fortress. It was located in northern Mordor, just east of Mount Doom, and was the greatest and most terrible fortified position in Middle-earth while it stood.
The first version of this tower was built early in the second age by Sauron after Morgoth had long been defeated and took more than 600 years to build. Depending on where the show decides to be in the timeline, there might be a fortress there already, but Sauron has yet to give it his personal dark-magic touch.
6 Lindon
Galadriel indeed told Celembribor and Elrond not to share any more information with Halbrand, but she didn't tell them why, and it's not clear whether or not High King Gil-galad knows either. Even if he does, he may simply ignore Galadriel, since it's been set up that he doesn't value her opinion.
It's more likely that Sauron will appear in Lindon, or one of the Elven kingdoms, in the guise of someone else. In Tolkien's books, he appears as the beautiful and talented Annatar, who claims to be an envoy of the Valar to impart wisdom and counsel. This is how he tricked the Elves into making the rings for him, and the show might use the same plot.
5 Pelargir
The people of the Southlands, who are now leaving Morgoth to found a new kingdom, still think that Halbrand is their long-lost king. Pelargir, a location that will be important to Gondor in the future, would be an ideal place to visit and recruit followers. Even just to plant a few believable rumors about certain troublesome elves or those pesky Numenoreans.
Halbrand visiting the western coastline would also help to explain how the humans of this region, and further south, would turn towards the Cult of Melkor and choose to serve Sauron. He also might stop there on his way to Lindon or Numenor.
4 Khazad-dûm
It's the place to be in the Second Age, so it would make sense for Halbrand to come here just for the networking prospects. The other issue is the precious mithril, and in Rings of Power, its special traits are derived from contact with a Silmaril.
Of course, Sauron is going to be interested in that, and given the power dynamics stressing out the royal family he has a lot of doubt, fear, and ambition to work with. The hostility towards the Elves, some of whom know his true identity, is another good reason to spend some time in Moria. All of that being said, it's also likely he's on a first-name basis with the Balrog in the basement.
3 Rhûn
2
There were once extensive Dwarf communities and settlements in this eastern region, but something happened in the Second Age to drive most of them out. This migration was positive in the sense that it strengthened the cities in the Iron Hills and Erebor, but negative because it indicated a profound social change in Rhûn.
The influence of Sauron and the Cult of Melkor grew stronger during this time. This might have been because Sauron went there personally to lead the cult and impart his own knowledge of craftmanship and dark magic. The cult would eventually spread across Middle-earth and grow in popularity in the Southlands, and even became the dominant religion of one of the most powerful kingdoms in all of Arda.
1 Númenor
Sauron isn't the one who eventually sinks Numenor, but his presence and influence were what decided its ultimate fate. He travels to the island kingdom as a hostage after surrounding to the far superior forces of Al-Pharazon and goes from a marginalized prisoner to a close advisor of the royal family. The people of Numenor are already prone to suspicion and greed, a fertile ground for the seeds of Sauron.
It was Sauron who introduced the Cult of Melkor to the people of Numenor, and it was he who designed and built the massive temple to Melkor that came to dominate the city skyline. He was there for centuries, bending the people to his will, until its destruction robbed him of the ability to take a pleasing form. It took him until the kingdoms of Gondor and Arnor were well-established before he could take any physical form again.