Whenever someone talks LA hikes it is always Runyon or Los Liones or something out in the Palisades, which for me from Atwater is a whole commitment with parking and traffic before I even start walking.
I want the close-in stuff. Something I can get to in fifteen minutes on a weekend, do a real hour or two on a trail, and be back before the day is gone. Eastside or thereabouts.
What are your go-to spots over here?
Elysian Park is right there and criminally underused. The trails behind the police academy loop up for decent views and you barely see anyone midweek. I go when I need to convince myself I am an outdoors person before returning to my desk.
Debs Park in Montecito Heights is my little secret, the Audubon Center trails are quiet and shaded and there is a small pond at the top that feels miles from the city. Free parking too which I always appreciate. It is not a big-view Instagram hike, more a peaceful walk-in-nature thing, but that is exactly why I like it.
From your side Griffith Park is basically your backyard and people forget how many trails it has beyond the crowded Observatory approach. Try the Fern Dell entrance up to Amir's Garden, way calmer, or the Mount Hollywood trail from the Griffith Park Drive lot.
If you want flatter and shorter, Silver Lake Reservoir loop is not a hike exactly but a solid two miles with people-watching and coffee at the end. LA really does spoil you with this stuff.
Elysian is the obvious close one and it is genuinely good!! But if you ever feel like fifteen extra minutes, O'Melveny Park up in Granada Hills is my favorite quiet one, way fewer people than Griffith and it opens up so pretty at the top. Bit of a drive from the Eastside so not an every-weekend thing, but worth it when you want real quiet.
Everyone covered the good ones so I will just add that Ernest E. Debs and Elysian are your best time-to-trail ratio from Atwater, both under fifteen minutes with actual dirt underfoot. If you have a dog, the Silver Lake meadow and dog park pair well with a reservoir loop. Griffith is the deeper bench when you want a longer day without leaving town.
I never took a hike over there, I looked into it, and certainly open to it.
The thing with Runyon Canyon is.. it’s close, it’s beautiful, yeah, parking sucks, but that’s the price you pay. I did the Glendale Peak and a couple other spots like Ascot Hills Park, but it’s just too much of a drive. It’s beautiful though.
But you have to admit, these are beautiful hikes that offer amazing views. 
Guilty as charged.