Native here who used to work in Santa Monica for years. It's totally doable - not too far. Just make sure you tell them to hold for late arrival. And yes, Shutters or Lowes are both fine. Right where you want to be. There's also the JW Marriott Santa Monica Le Merigot.
Also, since traffic sucks no matter what time you go leave yourself enough time to get back to LAX and through security. Believe it or not Google Maps has a fairly decent traffic indicator that will give you an idea of when you should leave.
Here's hoping you get a gorgeous day while you're here
