I bind all my work. The first wall hanging I did was without the binding but since then they all have had bindings. The binding isn't that hard to do once you learn or find the tricks to doing it.
On yours I'd either use the blue or the white from your blocks. I try to use a binding that either matches the last border and just blends in or one that captures a color from one of the blocks to draw attention to that area, and to make the whole piece just pop.
Good job on the one you are making!
Phyllis
QuiltingGrannie
Quilter's Pantry