Los Angeles: Griffith Observatory
This is an absolute priority place for people visiting Los Angeles for the first time.
Griffith Observatory sits high in Griffith Park area, giving a beautiful overview of the city. During the day time, during the sunset, during the night — there is never NOT a good time to check this place out. You can even hike to it if you're feeling adventurous. And honestly, that might not be a bad idea since parking can be hit or miss depending on the night. (I feel like this place has become more well-known and popular so the last two times I've been, parking has been a headache to find because it's so limited. Hiking would be preferred.)
Not only do they have telescopes to observe and look through, but exhibits are inside to educate about the solar system, and the Earth we reside on.
Access to the observatory is free. But make sure to plan ahead and get there early enough to reserve a seat for one of the featured shows in the Samuel Oschin Planetarium. This beautiful dome screen makes you feel like you're part of the environment it projects. I highly recommend "Centered in the Universe." I've seen it at least three times and I'm still in awe each time. The universe is just SO BIG. And I love how this video tells the different stories of it. The only bummer about the videos are they don't sell advance tickets — first come first serve — and they only have one planetarium, so the show viewings are at certain times. Make sure to check the times before you go.
On-going events can be found on their event calendar (such as star-gazing nights). Usually whenever I've been, there's always something going on.
And be careful about traffic and other events going on — especially around December. The first time I attempted to visit Griffith Observatory was when I was writing a story about it in my high school newspaper. Around December there's the DWP Holiday Light Festival in Griffith Park. I was unaware. And after choosing an exit of a long line of cars and then turning the wrong way off the freeway, my companions and I ended up on a 3-4 hour long excursion and never got to the park. It was awful. But eventually, some nights later, I found it and loved it.