First, I used thyme (perhaps a creeping time). It did fairly well, but it grew too high and the runners were too long (such that they began to cover the flagstones). I pulled it all out.

I then tried Wooly Thyme and it worked GREAT. It stayed short and it didn't spread out too far. The only problem was that I could not keep up with the weeds that grew within the plants. I couldn't possibly pull out every single "weedling" or I would have another full time job.

Now I don't know what to try next. I'm open to a iceplant as long as it stays short and doesn't send runners out all over the stones. I am also concerned if it flowers too much. We have a baby on the way and I don't want to worry about bee stings if he goes out to run in the yard. Any suggestions?

I DID notice that when I was using the Wooly TIme, the weeds were worst near the house (in that early-shaded section). In the higher sun area, the weeds are minimal and the Wooly Thyme did much better.

It's been a while since the OP posted this message, but I thought I'd comment. We had the same problem with the flagstone and the weeds, but we solved it by pulling up the flagstone, laying landscape cloth under it, and then cutting slits wherever we wanted to plant some groundcover. When we re-laid the stones, we left enough space in between to allow the plants some space to grow. The slits in the landscape cloth also tend to limit the growth. Good luck!