Is there a non-alcoholic substitute for rice wine?
The first choice would be a non-alcoholic mirin such as Honteri mirin, made by Mizkan, or the Kikkoman Kotteri, mentioned in the comment above. I have a bottle of Honteri mirin and on the bottle it states that it is a non-alcoholic mirin.

However, it should be noted that any of these products containing fermented rice can have trace amounts of alcohol. Even soy sauce can contain alcohol. From  Kikkoman :

Is there any alcohol in Kikkoman Soy Sauces?
Kikkoman Soy Sauces contain greater than 2% alcohol by volume. The alcohol is not added, but is a result of the fermentation process. Like wine or beer, our soy sauces are brewed and they are made from wheat, soybeans, salt and water. During fermentation, the wheat starches are broken down to sugars and part of the sugar is changed into alcohol.

So, while you may not see it listed as an ingredient, products may contain alcohol as a result of fermentation processes.
If you want absolutely no alcohol, there are a few other options such as white grape juice, a broth that complements the dish, or an additional amount of another cooking liquid used in the recipe. If your recipe only calls for a small amount, you could replace it with water.