"A Dream Within a Dream" is all about being alone. The speaker says goodbye to a woman in the first stanza, and spends the second isolated on a beach as he contemplates one of life's biggest questions: is what we see real? It sure sounds like this is something every person must deal with on their own time, by themselves, not in the company of other people. This may be because the answer to the riddle of reality requires some quiet time, or is just different for everybody. Plus, think about it: dreaming is something we do solo, so if life really is a dream within a dream, well, then were all alone for all of it.
Big questions about the nature of reality must be contemplated in isolation.
The speaker's lonely search for answers ends in failure, which implies that isolation may not be the best way to go. Just sayin'.