The Best of what Nintendo has to offer!
First off, if there are any families out there concerned with fantasy elements within media, I suggest you go and read J.R.R. Tolkien's essay on fairy tales.
Great Messages/Role Models - Link is a self sacrificing hero through and through. In the story he has already given his life in a way for the safety of his people. The game starts with Link waking up in something called The Shrine of Resurrection (Note that link did not actually die, but was severely wounded and needed to recover in this sort of stasis healing pod). Link wakes up 100 years after Gannon (the main bad guy) attacked the kingdom. Link failed to stop him and was gravely wounded. Zelda then managed to "seal" Gannon in the castle. While Link was recuperating, Zelda has been fighting Gannon in the castle for 100 years (presumable kept young by some magic used).
There is violence in this game. Link faces off agains monsters of all sorts. The message here is best stated by G.K. Chesterton: "Fairytales don’t tell children that dragons exist. Children already know that dragons exist. Fairytales tell children that dragons can be killed." Younger children might need to be guided by a parent to this meaning, but older children may find a role model in the character of Link. He stands up for what is right and seeks to destroy evil in his world even though the odds are against him.
Easy to Play/use: This is the hardest Zelda game to date. Definitely not for younger kids. That being said 10 year olds should find this game challenging but doable. Learning enemy patterns and combat is difficult at first, but will eventually be mastered. There are 120 "shrines" that present easy-difficult puzzles using the games incredible physics and environment engine. There are multiple ways to solve puzzles throughout the game which promotes creativity in all areas of play.
Consumerism - In this game you do collect a lot of items, but the majority of them are earned or found rather than simply purchased. An underlying theme of the game is exploration. The map is vast and any player will want to explore every single mountain top and valley just to see what's there. The currency of the game does play a big role in acquiring some items, but it is not the focal point of the game.
Drinking/drugs/smoking - There is one area where there is a bar and they tell you that you can't have any of their drinks because you are under age. In the bar there is one character who is passed out. This is a side quest that does not need to be completed and would most likely go over the heads of most children.
Swearing - No foul language at all
Sex - There are a few things to mention here. Firstly, in the game there are 4 great fairy fountains that player can locate. The fairies huge and dressed extravagantly with tons of make up and glitter. Like a form fitting sparkly bathing suit. They have large breasts but the game doesn't focus on them. They make comments on how Link is handsome and when they upgrade his gear (that is their function) they blow kisses, hug, kiss Link in a way that is to be seen as comical. They are not a huge part of the game, and you can literally play for hours and hours without encountering one.
Secondly, in the South Western part of the map, there is a race called the Gerudo. They are a race of tall, muscular women. (Think Amazon type). Tall (almost twice as tall as Link), dark skin (some are lighter). There are older, younger, and children Gerudu, and there are different body types as well (some are huskier and more heavy set, I give some props for Nintendo for including this). However, the majority of them are tall, slim and muscular. They wear baggy pants with an exposed belly and bra top. One of them is a Champion that Link knew in the past and is in a few cut scenes (but not in a sexual way, aside from here costume). A small detail that most won't notice is that all the Gerudo wear slightly elevated heels. A detail I wish wasn't in the game as heels are sometimes seen as "sexy." There is no love interest with any of these characters, but Link does need to disguise himself as a girl to gain access to their town because they don't allow men in. Again, this cross dressing is meant to be comical and makes no attempt to push agendas that are outside of gaming. The Gerudo are warriors and definitely do not take the whole "damsel in distress" role. Two of the champions that Link fights beside are female, so there are strong female characters present (more on that in a moment). Aside from the Gerudo and the Great Fairies all other female characters are dressed modestly.
A Damsel in Distress - One of the critiques of this game is that it promotes that men must always save women and that women need to be rescued. The main story of all the Zelda games is in fact that Link needs to save Zelda from Gannon. But more modern Zelda games put a different twist on it (In Legend of Zelda Ocarina of Time, Zelda actually disguises herself as a ninja type character to fight alongside and aid Link). In Breath of the Wild, Zelda is indeed in need of rescuing, but only because Link failed to protect her the first time they encountered Gannon, and she has been fighting Gannon on her own for the past 100 years while you recovered in the stasis healing pod. Part of the story is that Zelda has struggled to find the her purpose and power necessary to overcome the evil in the world. Only after Link fails to protect her, does the power become realized within her, and she uses that power to save Link from death at the hands of a monster. At first glance you could see only "man saving woman" but a closer look at the story shows that there is more going on. Two of the champions are female and were chosen to be champions because of their capability and skill in planning and battle.
Themes in Zelda: In most Zelda games the relic called the Triforce plays a major role. In Breath of the Wild, it is curiously absent save for veiled references. The Triforce is represented by three golden triangles each representing the virtues of Power, Wisdom, and Courage. These virtues were created by the Goddess Hylia (the supreme God of the Zelda universe) and represented by three lesser spirits or dragons depending on the game. In each game Link always possess the Triforce of courage, Zelda has the Triforce of wisdom, and Gannon (the bad guy), the Triforce of power. Gannon seeks control of all three so he can conquer the world. How he originally got the triforce of power remains unknown, but it can be used to teach children that power itself isn't evil, but if you have wisdom and courage alongside it, power can be a power for the forces of good in the world.
In Breath of the Wild, Gannon is depicted as a monster (in earlier games he was a Gerudo man but that's another discussion). The game states that in his lust for power he lost all resemblance to humanity and became an embodiment of Evil. There is no pity for this character in Breath of the Wild, only a driving need to defeat evil and rebuild the world it destroyed.
I hope this article helps you decide if this game is worth letting your kids play. This game is truly a masterpiece!