What tribe of Native Americans lived around the mission Santa Clara?
Because people would have gotten all confused if they'd put it in Santa Barbara. Anyway, the question has it exactly backwards. The Spanish missionaries were setting up a chain of missions a day's travel apart (along, or at least close to, what is today the route of El Camino Real). They didn't put the Santa Clara mission in Santa Clara... they put the Santa Clara mission near an existing native American settlement, and the city…
Mission Santa Clara was established because King Carlos the 3rd found out that Russia made a colony in Alaska. He didn't want Russia to come and take over California so he made settlements that were the missions. He also wanted to teach the native Californians the Catholic religion. So that is why Mission Santa Clara and all the other missions were established.
Mission Life In the late 1700s and early 1800s, mission lands were cultivated with corn, peas, beans and wheat. Thousands of acres were used as grazing land for cattle and sheep. Converted Native Americans (called neophytes) provided the labor to build adobe housing, The Alameda, and the San Francisco Presidio. In 1836 the mission was changed to a parish church and much of its land reverted to the public domain.
Misiones (Spanish for missions). Most towns and cities with Spanish names found in California, Arizona, Nevada, New Mexico and Texas started as small religious missions to convert the Native Americans found in such lands. One example of such religious buildings is the Santa Clara Mission, established in 1777 in Santa Clara, California (now in the middle of Silicon Valley).