Grey Worm was never the kind of character to wear his emotions on his sleeve. Sold into slavery before he could remember, he was raised to take orders and obey his masters, not to have thoughts and feelings of his own. After being freed by Daenerys, an overwhelming new world opened up for him: His people picked him as their leader, and others listened when he spoke. He had thoughts and ideas after all, could plan a siege, could advise a queen, could fall in love.
The relationship between Grey Worm and Missandei was one of Game of Thrones' most tender: two characters displaced from their native lands taking solace in one another. Throughout Daenerys' whole campaign, there was this background energy behind her of two people who loved each other fiercely, would follow their queen to the end of the world, and who hoped that, at the end of it all, they would be free to go live out the rest of their days in peace.
In an early episode in Game of Thrones' final season, during one of Grey Worm and Missandei's final conversations, she tells him that she feels there's no place for them (read: people of color) in Westeros. She planned to return east, to her home island, after seating Daenerys on the Iron Throne, thinking that her queen would finally be done with battles and wars and her army would be free to disperse.
Unfortunately for Missandei, the show had other plans for her, essentially using her as the switch that flips that makes Daenerys go crazy all over King's Landing. Missandei's death changed the course of all the lives around her, and for a moment there it looked like Daenerys was going to keep the Unsullied by her side, roving all over the world "liberating" people from their oppressors with fire and blood. It also seemed like Grey Worm was OK with that -- because he, too, was blinded by sadness and hatred to the point that he thought the only solace would be violence.
Where is Grey Worm going now?
Daenerys' subsequent death at the hands of Jon Snow freed Grey Worm a second time. Though he still loved his queen, and would always love her, he may have also felt some relief in being able to turn his back on Westeros forever. At the end of the season's final episode, "The Iron Throne," the Unsullied board their fleet of ships once again and prepare to cast off. Grey Worm tells one of his lieutenants, "We sail for the Isle of Naath," which might sound familiar for anyone who can still keep all of Game of Thrones' place names straight in their head. Naath was Missandei's home before she was stolen by slavers patrolling the oceans. It's a small, tropical island south of Essos, populated by gentle people and lots of butterflies. Missandei wanted to return there after everything was over, and it looks like Grey Worm and his Unsullied are planning to honor her by going there themselves.
What's Grey Worm going to do in Naath? Unclear. The island is a frequent target for slave ships patrolling Slaver's Bay, so it's likely that he's taking his army there to protect its people against future attacks. It would be a very sweet way to honor his lost love, and surely he'll have plenty of cleanup work to do since Daenerys left Essos in the care of her flighty lover Daario Naharis (remember him??!?!?!!). Grey Worm may be done with Westeros, but he's not done mourning his lost love, or continuing Daenerys' crusade for liberation -- though, hopefully, he goes about it a little more peacefully.