Genshiken, Watashi ga Motenai no wa Dou Kangaetemo Omaera ga Warui! Recommendations
These shows will show you the weird, creepy side of otaku... the part that make otaku what they are. (Obviously awesome!?) This is the stuff that makes normies cringe and who doesn't love that.
Even if you're just interested in otaku culture, these are good shows to watch. They're funny, you laugh at the characters and maybe even relate to them as well depending on your scale of otaku.
A note for Genshiken, it starts of focusing on the stereotypical male otaku but later seasons bring all kinds of otaku... yaoi fan girls(fujoushi) and cosplay otaku and so forth.
Both are series that are very relatable to otakus feelings and lives and make the viewer go 'Wow, that is so me!'.