I have a parking strip about 3-4 feet wide and 40 feet long, in morning and mid-day sun, in Berkeley, CA. A few years ago, we cleared out the old weedy grass, installed a drip system and large stepping stones, and planted woolly thyme for a low-growing filler between the stones. I LOVED it. For about a year and a half, it grew prolifically, flowered pinkly, and had no weeds at all. Best of all was that it smelled so great whenever you stepped on it. About six months ago it started to die off in patches, turning dead and brown even though the soil beneath it was damp. By now it's about half gone and weeds are popping up thru the remaining patches.
Our landscaper recommends good old hardy dymondia, which does well all over town, but I just don't like it. I prefer small green leaves. If anyone can recommend a low-growing groundcover/filler for our situation, please respond. We're on the way to replacing it all. Thanks!