One suggestion is to remove that trellis on both sides, and let the brick show, so it looks like it is part of the structure.

Yes! This is a somewhat old photo - we've removed the trellis on either side and now our roof is a deep charcoal black. Loved that idea!

More recent photo

Big improvement already! I like your mock-up of rich, mellow green shutters and triangle. Then paint the garage door itself a creamier off-white, or even khaki, to get away from the eye-glaring white it currently is. Also wouldn't hurt to spray paint the downspouts to blend into the brick.

Yes, such a huge difference with the trellis gone. So much better already I also agree, the garage door is too white, and the triangle above, should be painted what ever color you decide on for the shutters. The green may be a good choice.

What I'm hearing is definitely paint the triangle and shutters to match each other - love it! And possibly paint the garage door. I may consider replacing the garage door altogether! Thoughts on garage door colors/ designs? Thoughts on landscaping?