So, I have what seems to be a completely different take on this song. To me, rather than this song being about a relationship that isn't working, I see it as a relationship that is getting deeper.
"I walked across an empty land
I knew the pathway like the back of my hand
I felt the earth beneath my feet
Sat by the river and it made me complete"
The beginning is about being single and alone, which is a familiar place to this particular person. All they really needed was to be by themselves and "sit by the river" and think.
"Oh simple thing where have you gone
I'm getting old and I need something to rely on"
Now, this person is in a relationship and they're kind of questioning about whether it's right. They're wondering if they should go back to the "simple thing" and be alone.
"So tell me when you're gonna let me in
I'm getting tired and I need somewhere to begin"
After thinking about it, this person then asks their significant other whether or not they're going to let him/her in because they need to know that this relationship is worth it. They're tired of being alone but they need somewhere to start the relationship.
"I came across a fallen tree
I felt the branches of it looking at me"
At this point, I feel that the person has decided to commit to the relationship. I picture the "fallen tree" to be the only tree in the area at all, meaning that the person finally gave up the security of being alone and that the "branches" looking at him/her are trying to tell this person what they are leaving behind since the future with someone else is uncertain.
"Is this the place we used to love?
Is this the place that I've been dreaming of?"
Now both people in the relationship are looking back and thinking to themselves "Did I really like being alone?" And they're realizing that the place that they've been dreaming of is with each other.
"And if you have a minute why don't we go
Talk about it somewhere only we know?
This could be the end of everything
So why don't we go
Somewhere only we know?"
Finally, they decide to go talk about their feelings about the relationship. By admitting their real feelings for each other, it will be the end of the loneliness that was all they ever knew. Kind of like in P.S. I Love You where they're talking about the "end of life as you know it." Admitting their love for each other is the pivotal moment of their lives where nothing will ever be the same. And that "somewhere only we know," to me, is just the completely unique love that they share.
I know it's not what everybody thinks but that is what the song means to me. Everybody has their own interpretation. :)