I’d probably suggest Rurouni Kenshin (Samurai X) or Gundam Zeta instead. They have interesting themes, are more adult and have amazing art.
The Patlabor TV show is definitely much lighter material, a lot more accessible to children.
I think maybe it's the high-concept, almost frightening, aspects of GITS that resonated with me. But I understand why it's not popular with most people.
Obligatory Patlabor 2 opening title sequence: https://www.youtube.com/watch?v=IsMTpSDAGxM
Patlabor is slow, sure, and purposefully so (it has and deserves the reputation as being the "boring" mecha show), but cheezy? I haven't seen the TV show which I hear is a lot more comic, but I wouldn't call the original OVA/first 2 movies cheezy.
Wikipedia link (warning: spoilers ahoy): https://en.wikipedia.org/wiki/Paranoia_Agent
NGE can be philosophically heavy at times but is too diluted by its action sequences and fan service moments.
The first GITS movie is a philosophical tour de force and a piece of art that transcends time. A masterpiece.
It may also be that a lot of anime are series, and require a time investment.
The only other (comparable) anime that jumps to mind and something I can definitely recommend to you, is Serial Experiments Lain.