Given that I work in the geek sphere and am necessary exposed to what some might call an unhealthy amount of anime, I have some suggestions...
Blassreiter was pretty good. Apocalyptic near modern sci-fi.
Desert punk, basquash!(if you have any interest in seeing giant robots save the world by playing violent basketball), of the Gundam series I found 0080 War in the Pocket, and 8th ms team to be particularly impactful. Armitage III. Serial experiments lain for weird paranoid cyberpunk. I also absolutely second the suggestion of all of the ghost in the shell ever.
I can keep going if needed.