Whether you consider yourself to be a space nerd or not, there is plenty for everyone to do at the Griffith Observatory (4730 Crystal Springs Dr, Los Angeles, CA 90027). You can just wander around the grounds and admire the view of the city, and the Hollywood sign from here. Or enter the Observatory (free) and check out the astronomy themed exhibits including a Tesla coil and a camera obscura, weigh yourself to see what you would weigh on other planets and touch real moon rocks! There is an excellent planetarium show with live narration (you have to pay for the show and tickets are about $7 for an adult), which is well worth the price if you can afford it.
The Observatory holds some great free events including monthly talks on space science and astronomy and public star ‘parties’ where you can try out a variety of telescopes and get all your astronomy questions answered by local enthusiasts. Check the website for times and dates.
If you have plenty of energy left, you can walk the trail that starts just near the parking area for amazing views of the city. Just be sure to take plenty of water, sunblock and remember smoking is prohibited everywhere in Griffith Park due to the danger of fire in the park. Park rangers will ticket you if you are caught smoking and it’s a big fine!
The Observatory is closed on Mondays so you will be able to walk the grounds but not enter the observatory.