A gray/green (sage) would work better than gray/blue IMO. Another option is to use the lightest color from your brick.

You didn't ask but your shutters are too small. Each shutter should be half the window's width.

^Yes.^

I don’t really like the green we’ve got. Are there any blues that would work?

The brick is the one thing on the house that goes with the roof. Why would you want to paint it?

I can't imagine any blue that would work. You need to stay warm. You have 4 masses right now defined by color: roof, brick, wood siding, garage doors. Paint the garage doors to blend in with the brick and that will give some solidity and weight to the ground floor and make the 2nd floor peak less overbearing. Paint the 2nd floor a slightly lighter warm color (the cedar on the bay window works well). Now you will have reduced the house to 2 or 3 masses of color.

And, yes, lose the shutters.

I like the tan color of the trim. It looks dark in the second picture you posted. If it is actually lighter, get a darker version. You have two equally balance colors on the house now that can't be changed: the roof and the brick. Don't paint the brick. Go with a color that is close in color to the brick. (See how nice the cedar shakes look with the brick.) The trim could be a light cream.

I would not paint the brick . Instead , I would pull one of the lighter to medium colors and paint that color on the rest. That would give a nice cohesive look and make the house look less disjointed. If you really are liking blue , I do think that could work with your roof if it were a mid-range slate blue. In that case, I would still paint the garage doors a tan that blends with your brick.

My reason for painting the brick is that I don’t like all the brown, and painting it seems like the only way to take the exterior in a different direction from the tan/brown of the brick. I usually like the look of brick, but I don’t like this brick.

On my screen, the brick is not nearly so brown as the roof. The roof is super brown, and there is a lot of it. I actually like brown and brick and am so tired of seeing grey colors, but if I really wanted to banish brown, I would start with the roof. I hate the maintenance of painted surfaces, so I would never paint brick - maybe I would stain it - but never paint it.

Leave the brick and shingles alone. Paint the massive green section and the garage doors first then evaluate how it looks. Then you can decide if you want to paint the brick.