If taking the DASH bus to Griffith Observatory, where do we park our car? How long is the bus ride?
Most people who have a car and go to the Griffith Observatory dont go parking at Los Feliz and take the DASH. They just go to the Observatory and find parking there. People who take the DASH are often people who take public transit Metro or bus and catch it there. I've taken the DASH dozens of times and you hardly see anyone get on after the Metro station. Maybe at the Greek Theater stop, but hardly anyone in Los Feliz.
But you can try to find parking at Los Feliz. There are specific parking areas. You will likely find free street parking in the residential areas. but metered or limited free parking on the primary streets where businesses are located. The parking enforcement people often drive around and ticket cars.
If parking up at the Observatory is full, parking near the Greek Theater is recommended. I think it is free and you can either walk up the hill to the Observatory or catch the DASH bus at the stop near the Greek.
When are you visiting? Weekdays? Daytime?
Also, I know the observatory is closed on Mondays, but can you still go on Mondays for the view or are the grounds closed too?
Many people do Griffith Observatory as part of the Hollywood day. Park at Hollywood & Highland, stroll the walk of fame, see the star hand/footprints and any of the other H'wood Blvd. points of interest.
As you stroll Hollywood Blvd., you will either walk to a DASH shuttle stop (say at Barnsdall Art Park, 2.8 miles from Hollywood and Highland mall, or the Vermont/Sunset Metro red line station). You are walking/sightseeing anyway, so when you get to Thai Town along Hollywood Blvd, you'll be heading for that DASH stop to the Observatory.
If walking isn't possible, you can catch the Metro red line at Hollywood & Highland to that DASH stop, or Lyft line there (12).
When you visit LA, you'll want to park in a central area, for Hollywood that's Hollywood & Highland Mall, and walk or Lyft or city bus to the attractions in the vicinity. What you don't want to do is drive to each and every one of those venues, because you will waste too much time finding parking (which is limited at the Observatory). I'd even leave my car at Hollywood & Highland, hop a bus or catch a Lyft to La Brea Tar Pits, walk to the LA County Museum of Art, walk to The Grove/Original Farmers Market, catch a bus or Lyft back to my car afterwards.
Same with a beach day: Park in Santa Monica, walk, bike, bus between it and Venice/Marina del Rey. One doesn't get in a car and drive 2 miles to find parking at that venue. Trust me, finding parking in a busy city is a terrible waste of time and will frustrate you terribly.
The days of "nobody walks in LA" are over! With our great weather, park and walk/bus/bike/Lyft.