My somewhat spolier-lite to spoiler-free reccomendations:

Ghost in the Shell: Stand Alone Complex. I'd also recommend the original movie, but it's kind of a different beast.

Really well done series that switches between long expository plot sequences, and really well done action sequences, in a pretty good display of budgetary efficiency. The plot exposition, dialogue, and investigative stuff kind of surrounds the action scenes with an actual sense of consequence and meaning, relative to most anime that I've seen, and the series as a whole is kind of much more grounded than most other anime, which is also incredibly refreshing. The medium is used in this case more to emphasize subtle differences between this potential near-future reality and our own, rather than kind of just, being an engine for bombastic and outlandish animation and repetitive trope-work. The series bounces between episodically structured plots, or, stand alone episodes, and episodes that deal with an ongoing seasonal plot, or character plot, and there's a couple little progressions in there that kind of span the series if you're paying attention. There's not really any arcs, it's just a good, focused show, front to back.

The Venture Bros.

Slow start, but it's also probably one of the better pilot episodes, in my mind, of all time. Plenty of little comic book nerd references in there that are pretty enjoyable, and the comedy is pretty good at times while also tending not to venture into the offensive, except for maybe two or three instances that stand out in my mind, which is maybe somewhat impressive for an early adult swim show. I think, more than that, though, the series' ability to juggle serial plots and episodic plots is kind of mind blowing and insane. One-off episodes and single characters get spun off into entire fully formed characters with arcs and backstories. Stupid jokes get expanded into much larger things than you would expect. It's very well done.

Nichijou

Yeah, this one is pretty good, you should watch it.