I'll be staying in Culver City (close to the people I'll be working with) and so I guess most of my plans will be focused on the area since I won't be renting a car. I'm ok with walking or taking public transportation to places (as long as it's safe, I don't really know the area that well).
So recommendations on where to guy groceries or where to go out for a healthy lunch/dinner are also appreciated.
The Expo line (streetcar, partially elevated track) and express bus (733, red) are handy. Non-express LA Metro buses are orange, mostly. Culver City also runs its own bus system, green, and Santa Monica does as well, blue. All three agencies run service the Culver City area. They should all take the TAP card (contactless transit card). Culver City's buses shut down earlier than LA Metro's though. Anyways, use Google Maps, LA Metro's app, or the Transit app to help with route planning.
When I lived in that area, I did my grocery shopping at Ralph's, mostly, with supplements from Mitsuwa a little further down Venice Blvd and Simpang Asia (a place that's both a small Indonesian grocery and an Indonesian/American cafe/restaurant. Plus sometimes the local farmers market on weekends and Sprouts and/or Whole Foods.
It's not that long a bus ride down Venice to Venice Beach or Santa Monica; those might be good places for a jog on the weekend. They are tourist trap-ish and Venice Beach isn't much in the evenings, I don't think.
Also along Venice Blvd in the other direction are Arcana Books (mostly art and architecture books) and Surfas (great kitchen supply place, some fancy ingredients too).
I would also just load up walkscore.com and plug in where you'll be staying and working to figure out if there's anything worth walking to. Or, just ask the people you'll be working with for advice.