Can a comedy be good if it's not funny? After watching this show, I'm inclined to say yes.

Short version: I recommend Nichijou even if you're usually let down by comedy anime. Even when I didn't laugh a single time during an episode, I had a lot of fun. This series compensates for every joke that doesn't land with a unique, charming atmosphere that makes it immensely enjoyable. It's a classic.

I don't find most Japanese humor I've seen funny. Usually, when the joke is "this situation sure is strange!" or "look at that crazy reaction!" I find myself utterly disinterested and painfully let down. The kind of jokes anime most often tell can be done well, but they're usually not taken far enough to work (at least not by my culturally different standards).
Despite what I'd hoped when starting the show, Nichijou does not pull this style of comedy off consistently.
While watching it, I often found myself feeling like this guy:

Humor is largely subjective, and there's nothing wrong with having different kinds of comedies for different people. But humor is not the only thing a comedy can offer to entertain. Nichijou provides so much that I found it impossible to dislike it. Even when whole episodes went by with nothing I considered laugh-out-loud funny and even scenes that I found annoying, I wanted to keep on watching. There are three reasons for this:
One, the show did make me laugh a lot. The situations presented can be hilarious, and when the show does hit you with a punchline, it's genuinely good.
Two, the characters were for the most part enjoyable to watch and relatable.
Three, the stellar presentation creates such a compelling atmosphere that I wanted to come back to it again and again just to experience it. Central to that presentation is the music, which is memorable and gives every scene and by extension, the whole series life, as well as the animation, which is one of the best (and funniest) points about the show - expressive, inventive and often very satisfying to watch. (That's coming from a complete layman - I hope that speaks to the quality on display here.)

Nichijou is not only a Japanese comedy but also an absurdist comedy. This is also part of the reason why it works so well - an unfunny joke/situation was often saved by something absolutely ridiculous, often either as a background element, or a punchline. Absurdity makes the show unpreditable, which is crucial, especially in this genre.
The series plays with everyday situations, often using exaggerated animations - which fail to make me laugh in most other contexts, but are done really well here. I often found myself laughing because of how far they went to illustrate something that isn't funny on its own.
This juxtaposition of everyday situations, ordinary, very relatable issues with unique absurd elements and presentation is at the center of the appeal of the show.

If that sounds like something you might enjoy (and even if it doesn't!), I recommend you give Nichijou a try. I don't regret a second of my time spent on it - even though most of those seconds were not spent laughing.