My recommendations are:
1. San Francisco de Asis (also called Mission Dolores). In the city. Authentic, old, charming with a small cemetery. Limited grounds. This can be reached by cab or public transportation.
2. San Francisco Solano (also called Mission Sonoma). This is about 40 miles / 1 hour + north of San Francisco. A beautiful town in the wine country. A well restored mission. Has a special colleciton of paintings of all the missions. Historic Site (the Bear Flag was raised near the mission, beginning the split of California from Mexico). Many other attractions in and near the town.
Mission San Rafael (north of the city), Mission San Jose (in Fremont), Mission Santa Cruz in the town of that name and Mission Santa Clara are all in the Bay area. While each has its charm if you want something really special drive further south and explore San Juan Bautista (a wonderfully appealing mission located on the grounds of the only original Spanish Square left in California). It is about 90 miles / 1 1/2 hours from S.F. San Carlos Borromeo de Carmelo (also called Mission Carmel) is in one of the nicest seaside towns in California, a very popular get-a-way destination. The mission is exquisite, argueably the most beautiful of the missions. It was the headquarters of Fr. Junipero Serra. Great shopping and sightseeing in Carmel. Carmel is about 2 hours / 115 miles from San Francisco. You can visit both missions on the same trip but you will need to stay overnight in Carmel.