Peppermint loves wet feet and should do okay in these conditions. Although I'd still dig out some of the sand and mix in some mulch and worms to help improve the soil.

Sounds Like you might have a great place to have a bog?
Umbrellas plants warning these would take over the 3 by 3 space by the end of summer, Louisiana iris, Texas star hibiscus do well under those conditions but as stated above you might have to dig out some of sand and replace with more suitable soil.
Check out bog gardens this might suit your needs.

Here is a link that might be useful: bog gardening, bog plants, bog information

I would try a papaya tree, though it would not be evergreen in your area, but if planted now, will grow to about ten feet by September. They love sand and need plenty of water if planted in sand.

Another choice would be a miniature clumping bamboo. Evergreen, love sand can stand a lot of water, tropical looking, and you can use the canes as stakes if you like.

Kt

Last year I planted this near the drain spout from my fountain. The fountain needed to be cleaned fairly often because I don't use any chlorine. The plant dies back in the winter, and this year it is coming much bigger and fuller.

It's not hydrangea, but it is a tough guy and might be suitable for your area. I would dig out some of the sand and put in some better stuff, but unless I'm mistaken this plant is suitable to difficult soils, maybe someone else knows more.

Here is a link that might be useful: black adder hyssup

Thank you all for the great suggestions!

We got a downpour last night and the mulch that I'd spread in that area after planting the hydrangea had washed half way across the patio. Turns out that little bed is more like 4x6 rather than 3x3, so I may place a splash block or shallow container to catch the force of the rainwater and plant beside and behind that.

If this spot wasn't the first thing I see when I go in or out of the back door, I'd just put a trash can there and catch the rain water.

I'm still undecided about what to plant, but now I have some ideas...thanks to you all!

Ginger, Ginger, Ginger! That is what I would plant. I would plant the dark green that blooms pink and white, or the variegated ginger. Barbra

Could you trellis a climber in the corner?
You could plant salvia, daylily, and an assortment of bulbs.
Then mix in some annuals such as zinnia, cosmos, scabiosa, and cleome to fill it all in.
Having full morning sun and quickly draining sand is wonderful!
But you will have to get the deluge under control first.

Obedient plant - another plant that likes moist feet and will take over your space, but bloom for you in the fall. They don't mind full sun or a bit of dappled shade.

I am going to do a mix of things since it's a larger area than what I was thinking at first--if only to see what's happy there.

A trellis would be nice. I've been wanting to plant a clematis somewhere. And ginger, too. I've been trying to grow obedient plant from seed but haven't had any luck yet. Mint is something I've avoided because it's so invasive, but I should be able to keep it under control in a spot that's blocked on 3 sides--if it wants to grow under my house, that's okay!

I'm going to sink a big, but shallow, dish/bowl/trough (copper maybe?) into the ground to deflect the worst of the roof run-off. It can also serve as a cat watering spot.

Now I'm getting excited about this!