One of my faves is A Truly Vegan Restaurant, a Thai restaurant in a very dodgy neighborhood on Hollywood near the 101. Don't confuse it with the Thai place across the street with the Thai Elvis impersonator. It's a hike, so it's not that close.
I've also mentioned before how much I like the 101 Coffee Shop attached to the Best Western in the Hollywood Hills on Franklin. It is very vegetarian and vegan friendly.
At the Cat & Fiddle I recommend the ploughman's lunch (green salad with cheese & relish) and a plate of chips to share with friends; they have fabulous desserts, esp. some crumbly custardy thing. They also have Welsh rarebit, but I couldn't remember if it was any good. I think I had the vegetarian shepherd's pie. It was so long ago; I think it was merely decent.