If not overhung by trees that could encourage weevils maybe some bergenias or heucheras. Polyanthus primroses are another kind that like these first two produces evergreen leaf rosettes, and has the additional advantage of being found easily and cheaply at numerous outlets including grocery stores.

You might want to put in three or more kinds of perennials instead of having just one throughout the whole box.

If you can provide additional details of site conditions and desired attributes you can get more precisely targeted answers.

I've got a north/northeast facing area that I've been experimenting with a combination of sedums,hydrangeas,gold bleeding hearts, and hostas. One combination I really like so far is variegated 'Autumn Joy' sedum with 'Glowing Embers' and 'Nikko Blue' hydrangeas.

Here is a link that might be useful: {{gwi:243710}}

Thanks for the responses and ideas. boxofrox, the picture is beautiful. I love the combination. bboy, I think you're right. A combination would look really nice. I've never had bergenias before. I'll check those out. I do have quite a few heucheras and love them. Nearby plants are hellebores, saracocca, various ferns, azaelas, pieris japonica, camellias, and I'll have hanging fuschia baskets. The planter box is in the spot that gets the most sun in the yard, a few hours in the late morning, early afternoon. I really appreciate any help!

Might even be able to use it to display tuberous begonias. What other plants are right around the planter, that the new ones will be seen against?