I'm going to start with my nearest and dearest - the lovely, artsy, hipstery, oh-so-trendy area made up by Los Feliz, Silver Lake and Echo Park.
First up, Los Feliz:
Vermont and Hillhurst (between Los Feliz Blvd and Hollywood Blvd) make up this particular suburb, and are packed with vintage stores and quaint restaurants. Some of my faves:
Figaro - the best French food this side of France. Do expect slow service, but the big plates make up for it! I would suggest wine and cheese on a Sunday afternoon? Or a croque monsieur for lunch.
Little Dom's - brunch, with mimosas. I could do this every day of the week. An oh-so-tempting array of breakfast foods, plus your own bottle of prosecco and orange juice.
Rockwell - only go if they have a dinner show on. Some great local actors will keep you entertained with movie-themed performances, slipping in and around your table while you feast, with music from Baz Luhrmann's movies, or the best of the Coen Brothers. Really top quality.
Dresden - grab a drink here after a show at the Rockwell, or dinner at Figaro. Proper old-school Hollywood bar and restaurant, dating back over 60 years. The interiors are crazy good! If you ask really nicely the maitre'd may even give you a tour, and let you in on all the movies that have been filmed here. (Pic from the Google)
Vista Theatre - a vintage movie cinema in Los Feliz. One title a week, great old school theatre. Also check out Los Feliz 3 (the screens are tiny, like the real olden days!), just up the road.
Good Luck Bar - after your movie night stop off here for a great drink. It's another "hidden" bar, with a spectacularly Oriental interior. They make a mean martini.
Here are more hidden gems in Silver Lake.
Griffith Park Observatory - drive to the top. Get out wikipedia, read some of the history, it's actually pretty interesting. Walk around to the front of the observatory and marvel at the views. Best to do just before sunset. If you're feeling really ambitious, you can always walk to the top. Stop off at The Trails on the way down for a killer avocado sandwich, underneath the trees.
The Greek Theatre - part of Griffith Park, great outdoor theatre with a fun array of summer concerts! Google it.
The Hollywood Sign - best viewed from Beachwood Canyon. If you're really nice I will send you secret directions on how to get as close as possible, through windy windy backstreets, and some pretty impressive houses.
More in Los Feliz at Discover Los Angeles.
Blossom - Vietnamese food, let them lead you downstairs into the dungeon. It's worth it. Order the sake, and pretty much everything on the menu.
Bar Stella - the best damn cocktails I have ever tasted. My favourite is always the vodka gimlet (not pictured), but I'd recommend asking the bartenders for their suggestions, and then sitting up at the bar to watch them work. There's a definite beauty to it.
Still thirsty? Here are five great L.A bars, according to LA Weekly.
Pine & Crane - Taiwanese food, amazing wood-finished interior, fresh and delicious. If you can, go for lunch on a Saturday - the Silver Lake Market is right outside, and though small, worth a quick wander-around. It features about 10-15 stalls of vintage clothing and fresh produce.
Millie's Cafe - a proper roadside diner experience. Breakfast is a must.
More in the area:
Intelligentsia - with a line always out the door, one must imagine they make damn fine coffee.
Black Cat - stepping it up for dinner, great gourmet food.
Plus, the internet's guide to the best restaurants in Silver Lake.
So I'm fully aware that most of my spots are for eating. I like food, a lot. In an effort to even the playing field somewhat, here is LA Racked's 38 Best Independent Boutiques in LA.
Only got a couple of days in LA? This blog post from sfgirlbybay highlights some of my faves in the hood!
I'm sure I'll think of more to add, so instead of signing off, I'll just leave it at that. Have fun!
Also, you can see my other guides here: Silver Lake, Hollywood, Downtown, LA & Surrounds, and Tourist-ville.