What about some of the shorter daylilies, perennial geraniums or dwarf bearded iris? Dwarf narcissus such as Tete-a-Tete, February Gold, or Jetfire should do okay for spring color. Dwarf asters like Wood's Light Blue would give you some nice fall color.

I would also be relying a lot on foliage using grasses such as miscanthus, hakenochloa, festuca, arundinaceas or pennisetums. knautia macedonica is a sprawling scabious which will simply bounce back after soakings. Mat formers such as saxifrages, phloxes, campanulas are often impervious to downpours. It is actually hard to make good suggestions because I don't know much about your climate or soil type but rest assured, there are some good flowering plants which will perfectly suit your difficult circumstances. more details please.

Thank you both! I do like Irises and I never thought of grasses! I will look into all of your suggestions. The planting areas(strips, really)haven't been prepared yet. I currently have some planter boxes placed there, but nothing survives in the boxes over winter(below zero temps). The areas are covered with drain rock(by management), but do not contain drainpipe, just black plastic under the rock and what ever type of fill was used when they built the apartments. They are only 15" to 18" wide and about 6' long. I'm going to remove the rock, pull up the plastic, as it is partially decomposed anyway, and add amendments to the soil before planting. The West side gets full sun from about noon until sundown, the East side gets sun from about 8:00am until noon, then is shaded by the building. The building is faced with brick behind each area, the rest of the building is a yucky faded yellowy-beige. HTH

If you use tall grasses, they may bend (lean) away from the building, toward the sun. Also a heavy downpour may leave them lying on the ground. I would stick with short grasses such as festuca glauca. It is especially tough and a very prettty silver blue color. It is also widely available and cheap.

I have an eaves area without a gutter that is just one story, and it about 40 feet long, so I'll share my experience from somewhat similar conditions to yours. The water runs off my roof from any precipitation, both rain in the summer and melting snow in the winter and even drips after a heavy dew or frost. The power of all that falling water is immense, even from just one story. It batters plants (as you have found out) but will also churn up any bare soil, spattering onto the side of the building and creating a trench.

So here are my suggestions based on my gardening in this area for 10 years.
- Do not get rid of all the stone, since you will need to have all your soil covered in order to not make a mess with it spattering all over the building, foliage of what you have planted, and anything else in reach. Although typically I am not typically a fan of stone mulch, I'd suggest that you have a band several inches to a foot wide to accommodate the water falling in different areas depending on how the wind blows it and deep enough that no soil is visible. I'd also (after planting) mulch all the areas you have planted with the least moveable organic mulch you can find, such as long stringy bark that will knit together when it is down or perhaps pine straw. A lighter weight mulch will either spatter up onto the building or wash away. I usually use chippings from the guys clearing the power lines - free, and a combination of longer twiggy material and coarse, heavier woody chunks that seems to be relatively stable. You can cover the rock with the organic mulch if you want a uniform appearance.
- If you can, plant both in front of and behind the drip line as the plants coming from both sides will do much to hide the damage to plants in the path of the water from any particular storm. A couple of feet in front (if possible) would be a good minimum, but more would be better. I'm not sure from your description if this is possible.
- Plant things that will spread. That way if some of the plant is damaged by a particular rain event, the parts that have spread out will regenerate the area, filling in quickly compared to a new planting. I put in daylilies and a plant I haven't a name for as it was given to me by a neighbor, and they fight each other to fill the area. Perhaps something like gooseneck loosestrife which spreads voraciously and is impossible to get rid of would be appropriate here. Or mint . . . both have flexible stems and leaves.
- Consider both the flexibility and toughness of the foliage as well as how it will look when damaged. My daylilies aren't happy about getting battered as the leaves often break and seem to funnel water to the center of the plant, washing away soil from roots if I don't keep an eye of the mulch, so they mostly grow a few inches behind or in front of the worst of the water. The no name plant (large leaves shaped like dandelion foliage along with late spring screaming magenta daisy-type flowers) seems to somehow shed the water better; perhaps it flexes or wobbles more as the sheets of water hit the foliage. I've also thought about adding something with finer foliage since I think it might weather the damage better, though I'm not sure it will. For my area I thought about western Agastache in some of the drier areas against the building (though I'm not sure that any are hardy enough for you) or asparagus in areas with good soil.
- Consider how high up the damaging water gets. One year before the thuggish plants filled in, I grew scarlet runner beans , an annual vine, and they did well beneath my one-story eaves. The bright red flowers were a favorite of the humming birds and most of the foliage grew higher than the damaging water on a simple sting & bamboo trellis. I planted them inside the drip line, so had to keep an eye on water for them. I don't know if this will work with your two-story building.

Good luck. I'll watch this thread for suggestions to try out in my situation.

Ontnative, good point about the tall grasses. I bought some seed for a short blue fescue a couple years ago and never used it, but I don't know if it would still be viable. In any case, I do see it in seed racks often. Thanks for the reminder.

Nhbabs, thank you for the detailed response. I understand about the drip line. I tried to place my begonias against the building just inside the drip line, but the wind still blew sheets of water close in and decimated them. I had also considered using shredded bark mulch. I had it in some of my planter boxes to prevent splash-up and it worked pretty well. The drain rock has been in place so long that it's been filled in with dust and debris, and mud still gets splashed up onto the building. On one corner of the upper story the rain water comes down about 2' from the building and makes a puddle just outside the rock strip. I can't really plant anything permanent out past the rock area, as that is "the lawn" and it is mowed regularly by management. They allow me to have containers out there for veggies if I keep the grass trimmed around them. I reseed all the bare spots left when I remove the containers at the end of the season. They recently, after I don't know how many years, decided to have "the lawn" sprayed for weeds and fertilized. I had to place 'no spray' signs all around my little section of yard so they wouldn't kill my veggies.
I have a painted lattice panel at a right angle to the building(on the west side) attached to one of my planter boxes and I also had scarlet runner beans last year. This year I had a cherry tomato tied to it, but I think I will plant more scarlet runners next year.
Your mint suggestion made me remember that when we were living in the PNW I had a patch of Orange Mint just next to our front porch, and when we had rainstorms you could smell it in the house...it was wonderful! Yes, that might be something to have on the east side of the apartment where the begonias were...

Thank you all again. You've given me a lot to think about!