Were there any sedentary hunter-gatherer cultures in history?

Being sedentary as a hunter-gatherer is dependent upon having a reliable year-round food supply available locally, obviating the need to travel. This is not possible in all locales, but it has certainly existed in some places during certain time periods.

These places were unusually resource-rich and had multiple food sources. One example might be near a river, where there was plenty of vegetation (and animals feeding on it) on land, as well as fish in the water. Resource gathering could then shift from land to water seasonally.

In Europe, there was a rapid expansion of the population between the Solutrean and Magdalenian. Solutrean people were migratory big-game hunters, who followed the herds during their seasonal migrations. In the Magdalenian, the first settled or semi-settled villages in Europe appear. Later Magdalenian villages were pretty large, estimated to have populations of around 500 people. This is also when the first evidence of the division of labor appears in Europe.

These villages were almost always located on riverbanks, in places where the river went through a choke point or was especially suitable for fishing. Land resources were also rich in such areas, with plenty of edible plants and animals. Some are located near known migration routes for deer, so large scale hunting was a reliable source of food when the herds went through.

Gobekli Tepe is another example (from southern Turkey) that is often cited. It is a megalithic structure which possibly had a religious significance, and it was made about 12,000 years ago by hunter-gatherer people. These people were not only settled, they were organized enough to engage in large scale cooperative activity. Many of the stones used to build Gobekli Tepe are 12-20 tons in weight, and some were as large as 50 tons. These stones were quarried nearby, shaped, transported to the building site, and then erected by gangs of laborers. This must have taken a fair amount of organization.

In more recent times, there have been many hunter-gatherer communities that lived in settlements. Again, almost all of them lived near rivers or coasts. The indigenous people of the Pacific northwest are one example. Many people, such as the Chinook, Coast Salish, Haisla, Haida, etc. lived settled or semi-settled lives. This was made possible by the annual migration of salmon in the rivers, which provided a huge source of calories that could be preserved for use year-round. Additionally, there were plenty of other sources of food available locally, including marine and riverine, migratory herds of deer, and vegetation.

A good source for the Magdalenian period is the book The Magdalenian Household: Unraveling Domesticity (Ed. Zubrow, Audouze and Enioe) from the SUNY series on European and Mediterranean Archaeology.