Open air market on Grand Avenue in downtown with (almost) every kind of food. Grab a bite and a coffee or beer and post up here for a while. Angel's Flight funicular railway is across the street if you fancy a ride afterwards. Walkable to other downtown attractions.
Get some fresh air and panoramic views of the Los Angeles basin. Get tickets for the planetarium (surprisingly fun) or just bring a picnic and hang on the lawn in front of the museum.
**Arrive early if you want to find parking** Get some photos with the hollywood sign in the background. You can just park and take photos from the gate or if you fancy a hike you can trek up the hill and get surprisingly close to the sign!
Massive museum complex in the hills with lots of variety, a lovely outdoor garden, and impressive views. It'll take up a good part of your day, but it's definitely worth the time investment.
Walk the beach path from Pacific Ave & Windward Ave to see all the performers and merch stands or head east a few blocks to Abbot Kinney for cute shops / eateries :)
You will be aMAZEd.
Honestly my best recommendation if you're feeling ambulatory and wanna do something outside-the-box. Either pick up the book at Stories Bookstore in echo park or just go on one of the "free" walks you can download from the website. LA is littered with old staircases and pathways that used to be part of the old streetcar system. The streetcars are gone but all the staircases are still there hiding in plain sight.
Great outdoor patio Mexican food restaurant next to the LA River. Walk the glendale narrows river path afterwards and check out the river views and wildlife.