I'll go for the mulch. Raw wood will rob the soil, where it comes in contact, of nitrogen, as it naturally breaks down, like compost, but that may be of no concern. It might just look good. Sprinkling a bit of high nitrogen fertilizer before it goes down could give a nice look and not starve the plant.
Termites are everywhere. I wouldn't worry about their proximity to the house, as it should have a termite program, depending upon where you live. I read soewhere that if the earth did not have termites, its surface would have a layer of cellulose materials 100 feet thick.
Termites here in AZ are so bad that if you put a cardboard box on the ground with sommething in it to make good contact with the soil, the bottom will be gone in 6 months. Cattail prunings on the ground are covered in mud and gone in less time.
I'm no entomologyst, but the termites here have to be out of the light - hence the mud tubes and close contact with the box. Termites in your area
Good Luck!