In another life
Another place in time
It would be me and you against the world
Together we'd be fine.

The introduction is good, with you accepting that its only in another life or time that you guys would be joined hip to hip facing the world together.

The promises we made
We would see them through
Side by side, forever
It would just be me and you.

All the promises you guys made would come true, you would live the life you wanted. All troubles, you would face because you would be together through thick and thin.

Now as I watch you walk away
The tears roll down my face
I close my eyes
And long for another time and place.

But how the poem twists here, i really liked it. Suddenly things dont go as planned. Since its not the time and place all you hoped for can happen, you just wish it was indeed in another place. I loved how you express your feelings in this stanza.

All the memories will fade
Leaving hearts a little frayed...

You added some ryhming to it, which was very good and in the right place. The perfect ending to a well written poem.