Dulahey, I'd think of the planter boxes as essentially a large pot that you want to plant with perennials since you probably don't want to redo every year. Presumably you'll be watering these. I would plant several items in each side, ones that are tolerant of both sun and partial sun, since you have two different exposures. I definitely agree there should be symmetry in the plantings.

I believe I've heard the rule of thumb when planting pots is to choose a Thriller, a Filler, and a Spiller. So a wow plant, a background plant, and a trailing plant. For your situation, here's what I'd think about doing...

Prairie look:
Thriller: I'd think of something that will bloom all summer long, maybe may night salvia, or a coreopsis like moonbeam that you don't have to deadhead. Annuals would fulfill this requirement, too, but you'd need to plant every year.
Filler: a perennial grass that will give form during the winter, my favorite is ponytails grass (aka mexican feather grass) or even a hardy rosemary that will stay green year round
Spiller: golden moneywort is evergreen or semi-evergreen, depending on our weather, and has a nice lime color.

Cottage look:
Thriller: maybe a climber that you train over the mailbox? several types of evergreen clematis or maybe carolina jessamine would be cool.
Filler: dwarf nandina bush for year-round interest, or a small evergreen like a soft-touch holly or a dwarf boxwood
Spiller: Creeping phlox has great spring flowers and is also semi-evergreen.

I've read a number of threads about planting near mailboxes. The number one advice I have seen is to be careful not to plant things there that would be a draw to bees or wasps. Your postman will not be too thrilled to have to dodge them.

How easy is it to water?

Well, there is a small drip irrigation point in each bed that's attached to the sprinkler system. But I'm not going to run that thing more than once a week during dry hot summer spells. (water bill is high as it is)

But, I can easily drag the hose down there and water it as needed. The house is only about 50' off the street and I keep a hose right there in the front flower bed.

a boxwood on each side pruned to the shape of....well a box would look nice.

I like the different sedums. They don't need much water, and will create a solid mat that keeps the weeds at bay.