Natural food coloring?

Hibiscus flower infusions are a very intense pink, and are probably more neutral in flavor than beets, a nice clean tart flavor. The color is so intense you might be able to color food without noticeably flavoring it. The dried flowers are easy to find at natural foods stores. Here's a recipe for the delicious hibiscus drink jamaica:
http://www.101cookbooks.com/archives/000172.html
To make food coloring, you might try using a smaller amount of water to make the color even more concentrated.

Here's a great example of a cake that uses beets. It's pretty popular around these parts, especially for little girl's birthday parties.
http://www.nashvillescene.com/bites/archives/2009/06/25/the-beet-beat-vol-1-pink-radio-cake

Beet juice does add flavor to things, but it may not be the flavor you're thinking of. It doesn't taste like dirt or like it needs some goat cheese to go with it. It's more like a tangy kind of sweet-vegetal-ness. It's a nice pretty pink color too. Adding a small amount of boiled, peeled and puréed beets to cream cheese icing is actually quite delicious.

Think about foods that provide colors. Beets, carrots, berries, etc. However, most FLAVOR your dish as well. Hope this helped at least a little m