I've recommended these songs before for those seeking good Waltz tunes. "Iris" by Goo Goo Dolls is good, but maybe a bit fast.
"With You I'm Born Again" by Billy Preston and Syreeta is a nice one.
"Tennessee Waltz" works if you are interested in a bit of a country twang to it.
If you are looking for current contemporary, "James" by OAR seems to work fine, too, though it is also on fast side.
I've always liked "Hello Young Lovers" from King and I, with the Johnny Mathis version being pretty decent.And I agree with those who feel you can't go wrong with "Moon River."
Hope you find something you really like.