South of SFO Airport, where to eat?
If you have a car, then drive just a few minutes south to Downtown San Mateo. Go to B Street, and you will find a great variety of restaurants, many of which will do take-out. The side-streets also have lots of choices.
Here is a good website to get you started:
Enjoy and welcome to the Bay Area!
Downtown San Mateo is great with lots of variety. In Burlingame proper there's also some decent choice but not as diverse as San Mateo. A couple of places that come to mind, Broadway Grill, Straits and a bunch of nice Italian places. For Ramen and Japanese food, Ramen Club is very good. You'll have to look at the reviews...in particular Straits...up and down-ish.