What I heard on an Orthodox site (and with which, after thought) I must agree with, is that they go to be with the Lord.
Why wouldn't they? They have no sin. Remember, sin requires three things: knowledge that you are about to commit an act that is sinful, willing consent to the action, and taking the action itself. If any of these three are missing, you cannot say the person has sinned. For instance, if I take an action, not knowing that the Church teaches that it is a sin, there is no complicity or willingness to sin against God, and therefore, no sin.
Augustine's idea that babies somehow "inherit" the guilt of Adam's sin and therefore are condemned to an eternity in hell is . . . ahem, well, let's keep my opinion of this thought family friendly, shall we? Let's just say I find it contemptible on several levels.
Babies are born subject to death, as we all are. This is why Christ died, that by death He trampled death and made it of no account. It is Western thinking, influenced by Rome, that sees everything in judicial terms of guilty or not guilty and is consumed with the idea of punishment. As best as I can tell, Orthodoxy rejects this thinking (penal substitution) and the ancillary ideas and doctrines that come with it.
