There's a gate at the very end of Deronda Dr. In the Hollywood hills. Its street parking only but the hike up to the sign is about an hour. Definitely worth the effort.
It's called "Griffith Park" (not Hollywood hills) and the answer to your question depends on what area of Griffith Park you want to be in. Roads that go closest? There are roads inside of Griffith Park; all over Griffith Park. If you ask a more specific question I'll give you a more specific answer, I've been hiking through Griffith Park for over thirty years. If what your looking for are incredible views I recommend taking a drive along Mulholland. Especially if you're on a date, there are some really cool spots to just sit & chill with incredible views of the city below (views which probably inspired the song "Hollywood Nights" which also incorrectly calls it "Hollywood Hills"). If what you meant is "Hollywood Sign" - that's actually called the "Hollywood Sign" (not Hollywood Hills). Unspecific questions will yield unspecific answers. But I gave it my best guess as to what you're actually trying to find. Hope it was useful.
Use Hollywood Lane - Near Reservoir
Near as I could tell vehicles aren't allowed up there. You park at the Griffith observatory and hike, bike, or ride a horse in.
Thanks! Your answer is awaiting moderation.