Yes, this is for real. It's a museum dedicated to surfing. Unfortunately, it was closed (hours are somewhat erratic in the off-season). Housed in an old lighthouse, it opened in 1986. It contains surfboards and other surfing memorabilia. Open from July 4 through mid-September from 10:00 to 4:00.
Nearby is the Surfer Memorial, which I visited right before Halloween (hence the pumpkin stuck on the statue's head). Also close by is Cowell Beach. It offers some excellent views of Santa Cruz. And this is a fine place to watch real surfers.