Patlabor, specifically "Patlabor ON TELEVISION" and "Patlabor New Files" (sometimes called New OVA) are takes place in a very comfy near-future environment and is about a group of policemembers who are under the division for dealing with any mech incidents, meaning giant robot fights will happen in a very down-to-earth setting

I also recommend the movies if you enjoy the GITS movie as it's the same director and he likes exploring a various amount of social commentary, from criticism of institutional inefficiency to existential reflections, (just dont watch the 3rd movie, it has nothing to do with anyone who made the original Patlabor)

There's also the original Patlabor OVA, but I personally didn't enjoy that nearly as much as the tv anime, and some of the characters act a little different, so it might be jarring if you watch that before the tv anime despite it being chronologically made first