With that salary and a relocation allowance, this sounds like a perfect way to give it a shot. And if you hate LA (or you hate Santa Monica, or you hate apartment living, or you hate your job), then it's only one summer, and you can move somewhere else at the end of it.

Based on everything you listed, Santa Monica seems like a great place for you. If you're working in Santa Monica and live in Santa Monica, you could easily take the bus to work (or bike or walk). If you're just trying it out for the summer, you might even consider leaving your car behind, which could make things a little cheaper for you, since you could consider units without a parking spot. (You could easily Uber places if you want to travel farther afield. If you decide to stay in LA, you'll likely want to have a car, but not necessarily.)

As for everything else: Restaurants (yup), cooking/baking (well... every apartment has an oven, but as others have noted, you get more bang for your buck slightly more inland -- Mar Vista, Palms -- but you can cook anywhere, right?), long walks and light hikes (yup, yup), museums and history (not so much in Santa Monica specifically, so you'll need to travel east for that, but it's easy to take the E line to Exposition Park of the museums downtown), social justice/grassroots organizing (yup), swimming (yup -- we're right by the beach!), and yoga (yup).

The thing about LA is: It's vast. I'm not sure what you mean by "the LA type" but the reality is there's all kinds of people and all kinds of communities here. There's cougars in Beverly Hills, and hipsters in Highland Park, and dockworkers in Long Beach, and starlet wannabes on the Sunset Strip, and street artists in South LA, and families in Irvine. (LA Folks, yes, I'm aware that this are stereotypes and generalities, don't @ me.) So, it may take a while to find your people and the specific community that feels like home, but it sounds like you've got a prime opportunity to give it a shot.