Suggestions for lawn replacement

I'm planning to replace the grass in my backyard with something else when I undertake a massive re-landscaping project this fall. My last house I inherited a backyard full of 1" rounded river rocks, which worked very well although maybe not tops on the list from an aesthetic appeal standpoint, but since it worked for me before that's my default choice, but I want to evaluate other options before I do anything. The grass that's there now isn't terrible, but I don't like the idea of watering it all the time, plus it's a pretty small area so the dog tends to kill it by running back and forth on it, etc. Plus the backyard is at the bottom of a big hill, so it's quite an ordeal anytime I have to drag the lawnmower down there (and then back up again)

The biggest thing is for it to be dog-friendly--if it weren't for him, I would just do a patio and garden beds with some nice paths between them, but he needs an area to run around, etc (he was fine with the river rocks at the old place by the way). I don't want to do mulch because it's too close to the color of the "presents" he leaves for me so then I'd end up stepping in them before I could pick them up. And any sort of living groundcover is going to have to be extremely tough--it's hard for me to even keep grass alive in his area because of the dog running around on it and doing his business there.

If it helps, the house is white stucco with red trim (not Spanish style though--it has a shake roof instead of tile) and a gray Trex deck. Any ideas?