LotR -- Book 1 - Chapter 03 - Three Is Company

[Essex]

davem, re your question

Why doesn't Frodo dream when he's with the elves? And more importantly, why does Tolkien feel its important to point it out?

I believe Tolkien points this out to show how safe and comfortable Frodo feels with the Elves. Think back to what happened to Frodo that day. Almost accosted twice by a black rider. He could well have had a nightmare that night because of what he had gone through. But because of the elves proximity he feels safe. just swap the word dreamless for nightmare-less.......