When I think "stone streets," in classic fantasy games, I think "established, wealthy city." So a city with stone streets would be very different than the far more typical small village. I'd see a lot more shops and stone buildings than I would large swaths of grass.
Even "simple" cobblestone streets were very labor and resource intensive to build, if you think about it. How many cobblestones and how much effort would they take to line up and to dig holes for them and make a somewhat smooth surface from them? Imagine having you and several of your friends make, say, 2 miles of cobblestone streets, by hand (or with, at most, a few simple tools) and you'll see what I mean.
Then, if you wanted the road to last, there would also need to be some type of drainage so water doesn't sit under the stones. Instead, you want the rain to run off the sides. So it takes a lot of effort and planning to make good, stone roads, more than most typical fantasy villages will put in, unless they are part of a strong, established empire (think the Incans).
My point is: most average towns probably had a few dirt roads and more worn dirt paths, created by livestock or foot traffic.
Of course, if your city is set in a desert, and they're not living mainly in tents (I think a nomadic lifestyle is fairly common there), they would almost have to use stone or some type of pueblo architecture to keep cool during the day. But, even there, stone streets may not be that common, unless there is enough trade in the city to justify the effort involved in building a stone road.