I agree wholeheartedly with the above. LPKingsFan has some great suggestions, and the Captain is also spot on.
One thing to keep in mind, if you are going to Yosemite, do it on a weekday! Otherwise you may spend hours just getting into the park / valley floor area. It is being ruined by it's beauty and popularity, especially on weekends. Too many cars and no place to park them.
May is a good time for whale watching out of the Moss Landing / Monterey area as well. You can catch half day boat rides from Moss Landing and they don't have to go far out to see whales. I understand that May brings chances to see killer whales as well. The reason Moss Landing is better than Monterey? See the photo below - seafloor topography brings the upwelling food into the center of the bay for a more diverse ecosystem starting right outside Moss Landing - you can see just as much with shorter trips and they cost less as they aren't attached to the "Monterey" name.
I'm assuming you are from out of state (or maybe SoCal), but not in the general Sacramento / SF area. As such, some other options are the gold mining towns of Placerville (Hangtown), Jackson, Columbia, or Sonora. There are also underground cavern tours in these general areas for Moaning Cavern, California Cavern, Black Chasm Cavern, Mercer Cavern, etc. Moaning Cavern has the single largest single cavern in CA and when I was a kid you could rappel down from the ceiling to the cavern floor. It looks like they might be bringing that back soon.
The area is also rich with history, such as Indian Grinding Rock near the towns of Pine Grove/Volcano (go stop by Munnerlynns Ice Cream if you head that way!), Coloma (where gold was found, starting the famous Gold Rush of 1849), Sutter's Fort / State Indian Museum, Old Sacramento (historic riverfront area with a fantastic train museum), and other options.
If you like wine (or even if you don't), you can head up to the Napa/Santa Rosa area and check out the Francis Ford Coppola Winery and the rich selection of movie memorabilia from his films. If you do like wine, there are more wineries in that area than you could shake a stick at. Also check out the Charles Schultz museum if you like all things Snoopy - my wife loves that place.
Heck, if you have time you can shoot up to beautiful Lake Tahoe for a day.
Anyways, just a few ideas (depending on what you are looking for).