Look at the new varieties of buffalo grass. The one from Texas is called Techturf by the . The one from UC Davis and UC Riverside is called, UC Verde. Here is a picture of TechTurf mowed at 3.5 inches (and ready to be mowed again)...

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When it is mowed all the brown seed heads get cut off. Finding good pictures of these grasses is hard. My pictures of TechTurf are the best I've ever seen anywhere, but search for more pictures. You have to filter out the pictures of artificial grass)

There are several improvements of these varieties over the more wild (seeded) varieties. With these the seed heads (the brown things) grow at the same rate as the grass blades. When grass seed heads grow faster than the grass, people usually call them weeds, so this is good. The other is that these new varieties grow very densely. Seeded varieties grow very thin and allow weeds to completely blend in. The only negatives with buffalo are that it absolutely needs full sun. Up next to a fence or near a tree it will wither away. The other possible issue is the brown seed heads look like stickers but they are very soft. In my case I am allergic to them, but otherwise I would have it in my lawn (if I had enough sunlight).

You can also see the runners in the picture. Those are about 4 inches long. Any grass that sends out 4-inch runners between mowings is going to spread quickly, become very dense, and recover very fast from damage. It will also invade adjacent flower beds, so that's something else to keep in mind.

WOW! I just did a Google Image search for buffalo grass and found my photo above along with some highly misleading text. Here is the link. Contrary to the text, the variety in my original photo is NOT a seeded variety of grass. Seeded varieties look thin, like this.

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Looks like it does in the wild prairie to me.

buffalo grass does sound good but i would like a no-mow lawn.
sorry i didn't clarify that.

Buffalo grass can be grown as a lawn without mowing it. It will get a little taller than some people like lawns, but will probably stay in the 4-6 inch range at the tallest.

Consider seeding with Dutch white clover. It grows to 4-5 inches and stops growing. The white flowers attract bees, so that is a consideration. Also DWC never needs fertilizer. When it is grown with full coverage it looks very plush. Here is a link to lots of pictures.