That's the Griffith Observatory, which is located, perhaps unsurprisingly, in LA's Griffith Park. It turns out that those astronomy-loving tough guys Arnold beat up got off easy, because they were actually hanging out in MacGyver's backyard (according to his show's pilot episode).
"I built the place myself using a box of paper clips and a pack of gum!"
"Stop it, Mac. Just stop it."
Thanks to its futuristic look, Griffith Park has been a preferred location for sci-fi movies since 1935, including pictures like The Phantom Empire, The Man from Planet X, and Not of This Earth. We could show you pictures of those films, but you've never heard of them, so here are some Autobots clambering over the observatory in Michael Bay's Transformers instead:
DreamWorks/Paramount Pictures, DreamWorks/Paramount Pictures