The previous owners of my house put in a flagstone patio and filled the gaps, which range from 1/2 to 6 inches, between the stones with sand. Weeds grow pretty prolifically in the gaps, and the stones, which are quite beautiful in and of themselves, have become uneven and begun to break apart. I can't afford to re-brick the patio, so my second-best idea is to plant a thick ground-cover in between the stones to add aesthetic appeal, crowd out the thistles and quackgrass, and possibly keep the rocks more firmly in place.

I don't know much about plants, but I'm wondering if there's any cover that meets these criteria:

1. It must be beautiful. If it looks remotely unkempt or weed-like, my husband will say it looks trashy.

2. It needs to stand up to foot-traffic reasonably well.

3. It needs to be able to grow in sand.

4. It needs to spread quickly.

5. It should be hardy to zone 5a. Zone 4 would be better, but 5a will work.

6. It needs to be able to tolerate full shade to full/partial shade.

Geeze! Typing all this up it looks like a really tall order, but if there is such a plant, I'd be really grateful to know what it is. Would moss be my best bet?