The Alcove is squarely situated in Los Feliz at 1929 Hillhurst (Hillhurts) and Franklin. They have a great cheese store next door, which on occasion has the most amazing swiss ruby grapefruit yogurt. The desserts, mimosas and entrees are quite divine; the brie-apple sandwich and the potato pancakes are highly recommended (brunch only). The ice tea from last weekend was also really good. They've got a slightly sadistic seating system, so if you have pugilist friends, you can put them in charge of scoping out a table. Another plus is that they're open late, so if you're looking for something fun, but slightly more refined than Fred 62, they're a great choice.
Square One is across from the great-grandaddy Scientology HQ on Fountain Ave, just a block from the intersection with the ominously-named "L. Ron Hubbard Way". 4854 Fountain is more civilized on the seating, but has fewer seats, and the ones outdoors may be inadequately shaded. There's already been tons written about it, but I have to recommend the egg baked on grits with whatever seasonal toppings; for me it was mushrooms, cheese and young fava beans. It was really one of those incomparable food orgasms in my mouth. The pancakes with the amazing chocolate orange sauce is also excellent, but there's still that fruit butter with french toast I have yet to try. They're only open for lunch and breakfast, but they're so worth it, especially when you see their fruit salad has everything you were ogling over at the Hollywood Farmer's Market. Sadly the fruit salad is probably the only vegan thing there I have to recommend, as they're egg dishes are really really good.
The Alcove is accessible from any bus that gets near the Los Feliz area, but it's still a 5-15 min walk away unless you catch an elusive Hollywood DASH. The 180/181 stop at Vermont/Franklin. There's also the Sunset/Virgil intersection, serviced by the 2, 217, and 26.
Square One is really close to Vermont/Fountain, so the 204/754 and 217 will get you there.