I just finished planting/installing my pathway yesterday. I used Bluestar Creeper, Creeping Thyme, wooly thyme, and Red Creeping thyme. There are many options you could try, not sure what part of SoCal you are or what zone, so I am not sure what your best options would be. You may want some sort of moss under the gazebo. I mixed the typed of plants used so I could put the bluestar creeper in the spots where I thought it might get too much water for the thyme. I tried to make it very random looking. I then mulched the whole thing with a small gravel.

good luck

There's a groundcover that will take full sun as well as shade that I really like - Cotula 'Platt's Black.' I don't see it used very often in my area at all, for some reason, so I consider it to be rather unusual-looking. It spreads quickly via underground rhizomes. Beautiful foliage that resembles tiny ferns in green/bronze tones. Also goes by the name Leptinella squalida 'Platt's Black'.

Leptinella is an excellent suggestion - it is a very adaptable groundcover with an immensely appealling appearance. And is heaven to walk on with bare feet, also :-) Plain green forms are available if the dusky tones of Platt's Black are not to your liking - it can look a bit burnt under certain conditions.

The burned look can result from insufficient water - this is not exactly the most drought tolerant of GC's.