Was there any reason why Dr Soong chose for Data's eyes to be yellow? I can understand that he wasn't going for a completely human-looking android based on his skin color, but why yellow eyes?
In universe, I'm not sure there's ever been an explanation for why that specific color was chosen. However:
Data in an alternate timeline depicted in 7x11 ("Parallels") does have blue eyes instead of yellow.
Out of universe, when Brent Spiner asked Roddenberry why Soong couldn't manage to give Data life-like skin, Roddenberry replied, "what makes you think what you have isn't better than skin?"
Also, Spiner went through several makeup tests to create Data's eventual look: which is actually created with gold paint on his skin and gold contacts.
So, in universe, it could have been because the yellow iris material helped him see better than what more human-looking materials could achieve. This may have been similar to why Geordi eventually received occular implants with electric blue irises instead of more conventional coloration.
It's also likely that Soong deliberately avoided making his early androids look human. His goal was simply to create androids — fully sentient robots with humanoid form and personalities. His goal wasn't necessarily to create replicants of himself, which has even more serious social, moral and security implications. (Though he did eventually create a replicant of Juliana Tainer).
So they needed to be humanoid enough to be able to live amongst humanoids, but they weren't meant to be mistaken for actual humans. And seeing as humanity had already come into contact with alien species, their pale skin and yellow eyes wouldn't really be an issue for anyone.
If you have a copy of Larry Nemecek's "The Star Trek: The Next Generation Companion", there is one section under episode 13 of season one that states (humorously):
[…] The Jarada themselves became a casualty of budget problems; In the finished episode, they are only heard, not seen. Tormè had done a teriffic amount of work on the aliens, creating a hive mind culture he wanted desperately to depict. Still, Marina Sirtis. as Troi, gets a chance to do some linguistics coaching in this episode, and Spiner, McFadden, as Stewart all get to display their rarely used comedic talents. One detail in this script almost equals the "Chinese rice picker" explanation of Spock's ears from the original-series "City on the Edge of Forever," and that is the explanation of Data's skin color: "he's from South America"! […]
From the episode:
(to Picard, interrupting)
Hey Dix, what gives with this guy?
(leans forward, studies Data's face)
He ain't from around here, is he?
Uh, no... he's not.
He's from South America.
Yeah. He's got a nice tan.
Though humorous; Data was created as a humanoid not a human. He has a longing to become Human, but that is as a result of his programming and experiences. In some ways one can say the answer to why he is gold/yellow has as good an answer as why Spock has pointy ears. A human like alien.
Writers / Directors guide
Not directly about color; but the writers guide of TNG draw some of the lines of what is to become Data. It might be an interesting read.
Though it does not explain the color scheme directly it gives an indirect explanation on why the makeup as the one chosen could be taken.
From "Writers / Directors guide" by Gene Roddenberry, March 23, 1987 section "What is Changed: A New Crew"
LT. COMMANDER DATA An android so perfectly fabricated (by unknown aliens) that on applying for a Starfleet commission years ago he tested out as _alive_. This is a point of pride to Data, whose Starfleet psychiatric profile ("Medical eyes only"), lists the android as having the "impossible dreams of somehow, someday becoming human." With a phenomenal memory capacity, superior strength and similar assets, Data is an ideal Starfleet officer.
Further the in-depth section has this description:
MORE ON LT. COMMANDER DATA
Second in command of Number One's way team, Data (rhymes with "that-a") is an android so perfectly fabricated that only a skilled biologist would know he is not composed of normal flesh and blood. In spite of this -- or perhaps because of it -- he and GEORDI have become very close friends.
Data's appearance is that of a human in his mid-thirties. Until the role is cast, Data can be defined as representing any racial group between Pacific Oceania and the Middle East. Whatever his final physiognomy, it is a result of being manufactured by highly advanced (and never seen) aliens who intended him to serve as a repository of all the memories of a doomed Earth-Asian space colony. Unable to save those colonies from whatever exterminated them, the aliens of that world saved the memories of those colonists, resulting in Data being in effect the "sum" of the lost colony.
In giving Data the ability to handle so many memories, the aliens equipped him with other capacities they apparently considered "normal" (at least for themselves). Thus, Data has a memory capacity of phenomenal size as compared with humans, enabling him to serve both the vessel and away teams as something of a "walking library", his reading speed, manual dexterity, strength and vision are also superior to those of humans.
When a Starfleet vessel arrived to search for the colonists, they found Data alone on the planet. This was Data's first contact with any sentient life form, and he saw his Starfleet rescuers as a beau ideal of existence and decided to live in the same way. On taking the Starfleet Academy entrance exam, despite his difference from other candidates, he excelled in the entry tests and to date has never received a mark against his performance. (Starfleet's own regulations prevent the rejection of a candidate so long as it tests out to be a sentient life form.)
Data is of the male gender, fully functional, possesses the dominant emotional traits of his "parent-colonists" and appears to be absolutely incapable of falsehood. Generally, Data speaks in a more formal brand of English that the rest of our starship crew. He usually avoids contractions like "can't" or "wouldn't."
What is most appealing about Data is not that he is a machine, but that he is a machine who is eager and enthusiastic about adventure of life. To that end, he is an inquiry into the question, "What does it mean to be a human being?" Data's favourite story is Pinocchio -- he identifies himself with the little wooden boy who wanted to be human.