The artificial turf I 've looked at is quite spendy. Plus over over time I'm not convinced it wont fade from UV sun exposure and/or exposure to other outside natural elements.
Have you considered covering your area with landscape rock? No watering obviously. Once you tear out the old grass/weeds, grade it out, line it with a few layers of landscape plastic (get it at Wal-Mart cheap) so weeds don't eventually grow through, put rock a layer of 3 inches of rock on top and your done. You could do wood chips also but if your on a slope they could get washed away with a good rain.
Over the years my quest for the "perfect lawn" is starting to wear thin on me now. As said here already, its not cheap to have a nice healthy weed free lawn, even a small one. I'm becoming of the mindset now that I'd rather plant something like wild prairie grass and "just let it be" but that won't fly in my suburban neighborhood