I’m in Culver City and happy to see the love for the Westside.
While I do recommend at least one stop in K-town (Kyochon Chicken, for Korean soy garlic chicken wings), I do not recommend driving through K-town for a first-time visitor unless he has a local to show him around. My husband and I have lived here 10+ years and we love Kyochon, but we’ve only been there once because the driving/parking aspect is offputting. We’ve only been to one AYCE cook-the-food-yourself BBQ place and it wasn’t great, but if that sounds like your kind of thing, there’s a lot to choose from in K-town.
I myself don’t drive, but I echo the recommendations to rent a car. I have taken the train from Union Station to Anaheim, but again, I don’t recommend it if you’re new and on your own. Neither Union Station nor the Anaheim station is really in a tourist-friendly location. Not really dangerous, just not great if you don’t know your way around.
The Grove is ok if you’re fine with crowded places. Parking can be a bitch, but I like going to the Farmer’s Market for beef jerky, fresh meat, nuts, candy, etc. Avoid on Saturday nights if you dislike crowds. While there are restaurants here, this is not the place for ethnic fare. FWIW, The Grove is just north of the La Brea Tar Pits, a 5 minute drive.
For Japanese food, I recommend the Sawtelle Blvd area between Olympic and Santa Monica Blvd on the Westside. It is full of Japanese restaurants and shops. We go there all the time for Japanese curry, ramen, and gyoza. I also really enjoyed my trips to the Little Tokyo area of Downtown LA, but I’d say if you’re staying on the Westside to just go with the Sawtelle area.
For Chinese food, I recommend Chinatown near Downtown LA. Parking is a bitch, but the best Chinese food I’ve had in LA is here. It’s been a few years, but Yang Chow was great last time I was there. If you like soup dumplings (xiao long bao), check out Din Tai Fung at the Americana in Glendale or ROC Kitchen in the aforementioned Sawtelle area.
Not sure if Cuban is your kind of thing, but there’s a place called Versailles that has delicious garlic chicken, served with black beans and rice and plantains. It’s by far my favorite discovered cuisine in LA.