"Warm exotic beaches" aren't words usually associated with the Bay Area, but there are a few places that might just fit your criteria. Santa Cruz
has the warmest beaches in the Bay Area, and of these the beach at Natural Bridges State Park is the most exotic. At one time, there were three arches here, but erosion has done its work, and there's only one left. Still, it's a very scenic beach, and during the fall and winter months Monarch butterflies
At the Santa Cruz Beach Boardwalk, you'll find one of the few beachside amusement parks left in California. There's a classic wooden roller coaster, and a vintage 1911 Looff Carousel (which has been designated a National Historic Landmark).
Waddell Beach to the north of Santa Cruz is popular for such exotic activities as wind surfing and kite surfing. But because it's windy here, it'll also be colder.
There are also some Bay Area beaches that aren't particularly warm, but have exotic features that are worth mentioning nonetheless.
The most exotic San Francisco beach
has to be Baker Beach, with its dramatic views of the Golden Gate Bridge. It's probably the warmest beach in the city. Farther to the south, Fort Funston is notable for its hang-gliding port. There's an observation deck where you can enjoy the view.
To the north in Marin County, Point Reyes
is not particularly close, about a 1.5 hour drive from Oakland, but it's still notable for its wild dramatic beaches. Drakes Beach is very scenic, backed by sandstone cliffs, and along with Limantour Beach is one of the warmest beaches at Point Reyes National Seashore.