I'll be frank: Nichijou is, without a doubt, the greatest anime I have ever watched in my 10+ years of watching anime. I'm going to give a list of the reasons why I believe Nichijou to be the best anime ever created, and why you should watch it as soon as possible.
1. The jokes
Probably the strongest reason on this list, the jokes are the main part of why I believe Nichijou is so amazing. They are perfectly timed and spaced. Every single funny moment is delivered with nearly flawless pacing and delivery. Ordinarily, jokes likes the ones in Nichijou would be labeled as "weird japanese humor", but the way the jokes are executed makes them perfectly relatable to an english audience (I'm from the USA). From simple punchlines, like the professor throwing a bucket of popcorn and hitting Sakamoto in the face, to episode-long running gags like Nanase's shoe in the first episode, there's something for everyone, and I have yet to find someone who doesn't at least crack a smile during an episode.
2. The characters
They don't have the typical attractiveness appeal of the typical "japanese schoolgirl" trope. Instead, the characters are likeable through their personality traits and their actions. Mio is the average student with a crush on her senpai. Yuko is the slacker who can't seem to stop getting in to trouble, but strange things constantly seem to happen to her. Mai is the cryptic joke factory who will always keep you guessing on what her true intentions are. Each of the characters have their own charm and appeal, and the chemistry between characters keeps the show interesting and enjoyable.
3. The animation
At first, Nichijou seems like it's animated at an average level - no massive bucget, but the animators are still passionate about the show. But then you get scenes like the "Safe" scene, with huge, over-the-top effects and animations that really contribute to selling the joke. Additionally, between scenes, there are blurry but gorgeous stills of scenes from around the city the characters live in.
4. The OP
This one is pretty simple. Nichijou's OP is one of my favorites. It's catchy, the animation is fun to watch, and it's the ONLY anime opening I never skip, and find myself singing along with every single time. If the point of an OP is to make the viewer excited to watch the show, then Nichijou has a perfect OP in my opinion.
5. The story
The story in Nichijou is certainly not deep - it's a slice of life. However, amidst all the jokes and strange events, there is still a clear storyline. Mio has her hidden affection for her senpai, Yuuko has her grade issues, Sakurai and Takasaki have their strange almost-romance, and so on. Every character has a problem they want to solve, and whether or not they solve it keeps the show moving forward. However, Nichijou does a great job in not letting the story take over and get in the way of the jokes. Personally, I don't care much for romances in anime, but I was still able to enjoy the romance stories in Nichijou because they were constantly interspersed by weird happenings and strange coincidences between the supposed lovers.