Neil Armstrong had ten grandchildren according to this article by the Guardian. The only one mentioned in the article is Piper Van Wagenen, who spoke at the memorial ceremony the article covers. Given that they are still quite young, I suspect that you aren't going to be able to find any information outside of articles such as this.

Don't take this the wrong way, but that seems like information that you shouldn't be able to just grab off of the internet. They aren't public persons just because they had a famous Grandfather, and are entitled to their private lives in anonymity. Genealogy sites, for the most part, don't allow access to that information on personal family trees for that reason, so while the Alaskan's suggestion isn't a bad one, I don't believe you will be able to access the most recent generations without permission from the tree administrator.

Have you tried a genealogical website? Something like geni or myheritage or ancestry.com could have what you're looking for.