Mammoth Lakes is California's not-so-hidden gem. While you'll often hear folks in SF suggest "Tahoe" or "Napa" for a fun weekend trip, Mammoth comes up much less often... and I'd prefer it staying that way. But in fairness to you — now you know!
Bring
CamelBak
Great for hikes (duh, but worth reminding).
Endurolytes
Endurolytes (or any electrolytes) are awesome, and they work. Helps in acclimating to the slight elevation change from the Bay Area.
Use
AllTrails has some great hikes around Mammoth Lakes - think of it as Yelp for hiking.
Stay
Phenomenal private residence, if you get the chance. Great, spacious accommodations, excellent location, & staff will drive you/pick you up from wherever. Rent some electric bikes so you can cycle up some mountains.
Eat
SKADI Never got a chance to visit, but consistently heard from locals how good it was. Saving for next time.
June Lake Brewery
This place is awesome. Really lively atmosphere, great selection on draft, & really cool packaging. Pay a visit if you can, as there are many food options nearby and places to sit. Friendly crowd.

Ohanas395
Fantastic poke, one of the best I've had in California.

Visit
Spooky ghost town. Really cool to visit and experience history. Not often that you get to walk through and literally touch the exact same buildings Americans inhabited in a gold rush centuries ago.

Gull Lake
This is my favorite lake in the area. It's relatively small and unassuming, but it's beautifully still. You can rent a kayak for a few hours for relatively cheap. There's a rope swing on the opposite end for younger kids. You will feel at peace.

Emerald Lake Trail
Beautiful hike that ends in a lake that literally looks jade-green. Not short, not long, but beautiful views.

Rainbow Falls Another hike that locals mentioned is the most popular; we never visited but will do so next time.
Do
Ski
Tahoe's (lesser-trafficked) equal.
Hike
Just go outside. It's why you're visiting, after all.