What's wrong with a frame? They are (or can be) made in thousands of ways from minimalistic to ornate...to complement the work or your decor. Photos and flat art, such as watercolors or drawings, are often matted in the frame. So, even though it's "just a picture frame" it doesn't have to look like any old picture frame. But there are frameless options, too.
Is this a photo or a painting?
Photos can be mounted between sheets of glass or acrylic and hung without a frame. Paintings on canvas are sometimes mounted on thicker strechers and are displayed without a frame. A photo can be displayed the same way by printing it on a canvas-like material. It's called a gallery wrap.
Then there's dry mounting, where the photo is pressed onto a foam core board or other substrate. The board is usually about ⅛–¼" thick, white, and is meant mostly for framing or other non-artistic display. But some photos are sharply displayed by mounting them on a much thicker board (½" to 2", one brand name is Gatorboard) with a black foam core, exactly sized to the photo.
If you want some ideas, one of my favorite art supply sites is DickBlick.com