Do you want to start with more traditional sushi, or more creative (new-wave) sushi? I think if you are truly serious about your sushi edification, then the saying “To know where you’re going, you need to know where you’ve been” applies here…
If you agree with the above strategem, then you should try the more traditional sushi places first. Learn how sushi was made originally in the old days. Get used to the terms/lingo. Also, armed with such knowledge, you may be more adept at enjoying the more creative stuff later on in your journey.
Need I remind you that the quickest way to learn is by sitting at the bar? (Furthermore, doing omakase often facilitates more banter between you and your itamae).
Having said all that, here are some traditional “starter” places (not too hoity toity, as per your request):
Sushi Gen (J-town)
Nozawa Bar (Beverly Hills)
Sushi Kimagure Ike (Pasadena)
Whatever you decide to do, savor your adventure! And please report back!