There is no "Mission San Rafael Arcángel in Rafael." The mission is located in the city of San Rafael, California, in Marin County, north of San Francisco. The city took its name from the mission, not the other way around.
Native Coast Miwok neophytes lived on-site, learning agriculture (wheat, corn, grapes, olives), cattle ranching, weaving, carpentry, and Catholic doctrine. The mission's hospital function treated both natives and settlers.
The mission church replica stands at 1104 5th Avenue, San Rafael. A small museum displays artifacts. The site is California Historical Landmark #220. The city of San Rafael (pop. ~61,000) grew around the mission plaza.
The mission gave the city its name—so you'll find it in San Rafael, not "Rafael."