Floating here like this with you
Underneath the stars aligned (at night?)
For 13 billion years the view
It's beautiful, and ours alone tonight
Underneath the stars

Spinning round and round with you
Watching shadows melt the light
Soft shining from our eyes, into (a tear?)
Another space is ours alone tonight
Watching shadows melt

The waves....break
The waves....break

Whisper in my ear, a wish
"We could drift away so far"
Your voice inside my head, a kiss
It's infinite, and ours alone tonight
Watching shadows melt or We could drift away
(Depends upon which version you're listening to)

Flying here like this with you
Underneath the stars aligned (at night?)
For 13 billion years the view
It's beautiful, and ours alone tonight
Underneath the stars

(swirling echo voice: Underneath The Stars)

With everything gone
And all still [bad word] 
Together as now
Forever as one
In each other's arms
So near and so far
Together as now
Underneath the stars

As the waves....break

This is the best I [bad word] up with. Some of the words are probably wrong, but I THINK it's a pretty good start. The Kansas City and Denver versions are each different in certain places, but I'm going with the Denver version here. Thanks to Brian for providing the clearest version yet, that helped a great deal with the deciphering.

Update: I'm now basing these lyrics on the Dallas version. Again, some words are different from the previous versions.