To seek pleasures other than sexual (which is sometimes the case also for not castrated men).
The below fragment from A Wiki of Ice and Fire is about the Unsullied you mention (in the book he is called Stalwart Shield).
Note that this a Wiki about the books, not the TV series, so it may contain spoilers.
Stalwart Shield would occasionally go to a brothel in Meereen where he would pay women just to lie with him and hold him.
movies.stackexchange.com/users/19042/Chanandler Bong
Daario Naharis mentioned that his mother was a whore, and I suppose some of The Unsullieds have similar background as they grew up in a brothel.
Having a woman hold them and sing for them, stroke their hair may remind them of the feeling of having a mother.
movies.stackexchange.com/users/20448/user20448
No, in the books it is clear that The Unsullied have "neither root nor stem."
But they are still people.
They are still men.
They may still long for human - and female -contact and may fantasize sexually even if they have no sex organs.
movies.stackexchange.com/users/20445/Ygritte Snow
There is more than one form of castration: there are testicular and penile.
The Unsullied are not castrated totally.
This even comes up in the show when Daenerys asks her handmaiden if it’s the root and the trunk, or just the root.
She replies, “I do not know.”
But in the books, there’s a mention of it as some point which makes it clear that it’s just the testicles.
This was thought to have a focusing effect on the discipline of the soldiers.
And while it does affect sexuality, it doesn't do so totally.
In other words, a person who was had their testicles removed could very well be more or less sexually normal.
They can still achieve erections and will ejaculate (just without any sperm).
There are some famous US cases of rape offenders being castrated in this way, then being released and surprising everyone by committing rapes again.
movies.stackexchange.com/users/20439/msv
Answers to this question have been suggested have been given a few centuries before A Song of Ice and Fire was written: Cleopatra: Not now to hear thee sing; I take no pleasure
In aught an eunuch has: '
tis well for thee, That, being unseminar'd, thy freer thoughts May not fly forth of Egypt.
Hast thou affections?
Mardian:
Yes, gracious madam.
Cleopatra: Indeed!
Mardian: Not in deed, madam
; for I can do nothing
But what indeed is honest to be done: Yet
have I fierce affections, and think What Venus did with Mars.
So, while they cannot service their affections in deed, they may service them indeed.
(And indeed, in deed, since George R. R. Martin allows his characters a sex-life less focused solely on penis-vagina penetration than Shakespeare did Mardian).
(That's assuming that Mardian was even lacking in a penis as well as just testicles.
In the days when castrati still sung, they had an advantage in illicit affairs in that not having testicles is a very reliable form of contraception).
movies.stackexchange.com/users/20474/Jon Hanna
In  Game of Thrones  S05E01 "The Wars to Come", one of the Unsullied is shown to be visiting a brothel. Missandei has also mentioned that she has heard that "more than one Unsullied has been known to visit Meereen's brothels."   I have the same question as Missandei's to Grey Worm: Why would an Unsullied go to a brothel? (Aren't they castrated, and would derive no pleasure from the services offered by brothels?)
Why would an Unsullied go to a brothel?
movies.stackexchange.com
<game-of-thrones>
movies.stackexchange.com/questions/33215
movies.stackexchange.com/users/1006/galacticninja
He would occasionally go to a brothel in Mereen where he would pay women just to lay with him and to hold him. Stalwart Shield would occasionally go to a brothel in Meereen where he  would pay women just to lie with him and hold him.  
 To seek pleasures other than sexual (which is sometimes the case also for not castrated men).  Stalwart Shield would occasionally go to a brothel in Meereen where he  would pay women just to lie with him and hold him.  