Los Angeles is often misunderstood, but I think it just takes time to reveal itself. We've always used it as a halfway stop when travelling from Australia to buy coffee in Central or South America. We like it so much we're opening our second LA Paramount Coffee Project in September.
A hike is a very LA thing to do, even if it's just for some celeb-spotting or to work off last night's In-N-Out cheeseburger with "animal" fries (extra sauce and grilled onions mixed with your cheese; it's off-menu - do it). The Runyon Canyon is our version of the Bondi to Bronte walk; from the top you can see across the whole city.
When out-of-town friends visit, I take them to Grand Central Market: lovely acoustics, really nice light, a diverse mix of operators and customers. Go hungry. Go for a Reuben at Wexler's Deli - it's got the right level of acidity, fat and smoky-pastrami goodness. At Villa Moreliana, don't be surprised if you're handed a carnita or a couple of tacos while you're waiting in the queue. For coffee, perch at G&B's bar. Eggslut is another great breakfast option - people queue forever for their egg and bacon cheeseburgers.
Grand Central Market.
It's an LA habit to go to one place to get coffee and another place to get breakfast. By contrast, Go Get Em Tiger, Sqirl, Gjelina and PCPLA do food and bev with equal excellence - a fairly new phenomenon for LA.
A great café needs not to take itself too seriously and should deliver something honest and original that the community wants to be part of. Destroyer in Culver Cityis really hot right now. It does brunch and lunch on weekdays only and it's close to the airport - you could make it your first stop.
Downtown is having a resurgence right now and Ace Hotel is a great base to check out the transformation. The United Artists Theatre next door is worth a look, too; they have great talks, gigs and recitals.
To celebrate while not dropping too much cash, the chicken sandwich and Thai chicken wings at Night + Market Song are always bang-on. These guys, with their original take on Thai food, are rock stars at their craft.