Paintings like this often can stand alone.

You might try on another paper, a border of some kind. Not too busy. And see if that strikes you positively. Just do one side, and use faint colors if you use color. If you mat this instead a ruled ink border of one or more thicknesses of lines may work.

For adding stuff to drawings and paintings I always use tracing paper over the almost finished work, to try things. You have to be careful at this stage, and not get trite or corny. (if anything a few sea birds in the distance suggested, may be enough.)

Unframed paintings can look like they don't have "their clothes on"... a mat with a thin border like the museums do, often finalizes things. Often for acrylic or oil, they only use a linen liner and that minimal texture is enough.

The two worst moments in a pictures life:
1) the blank canvas at the beginning
2) the last touches or not

When pictures have minimal content, whatever the content is, should become the design device. In your siggie, the beach zags into the picture and provides that movement. In your finished new piece, clouds can do that for you and or the waves. Our eyes move around a flat 2 dimensional surface and learning how that works often then gives you a foundation for when a piece is finished. Also in your siggie the left movement created by the distant mountains to the right, is checked and the right hand darker mountains, bring the eye back to the center by being darker and shorter. So in effect the viewer's eye remains in the picture and settles on the receeding horizon of the beach. That photo is a good example of keeping the eye inside the picture. An unsettled composition, might lead the eye off the plane and out...and unless that is a desired dramatic effect, should be avoided in many instances.

One learns this in design class. Since you are doing this yourself, check out some art design places. I used a book long ago by Rudolf Arnheim....The Art of Visual Perception. At the time there was very little out there...today there must be newer easier type books.
Amazon is a good resource:
http://www.amazon.com/Art-Visual-Per.../dp/0520026136
And try the net in general. I was mostly self taught, but I did attend art school on the College level when hubby was in Vietnam after my professional training was done. I was behind the kids who had alot of art training in high school and at home. So I used some books to point me and minimize the failures that are so rampant in producing art.
(this really helped me with photographs too!)

I think in this painting, your use of color has become the main object.
So adding something might change that considerably.

This book looks interesting and may be less pithy than Arnheim:

http://www.amazon.com/Vision-Art-Mar...p_ob_b_title_1