Danganronpa is absolutely fantastic but it's hard to really call it a visual novel since it has gameplay. But a large amount of the game is told in visual novel format so I guess you could call it a gateway drug to VN's. 
But yeah, definitely pick it up if you're interested. If you want to try a full-on visual novel though I suggest The House in Fata Morgana to people anywhere I possibly can, it's amazing.
I like to refer to them as interactive visual novels.
Eeeeeeeh I'm going to say yes and no on recommending this as a starting place.
Danganronpa 1 was both good and not so good. There are some moments of writing, be it an idea presented, a character saying something, or saying nothing, that are really well done. It has a large cast of characters, and there are sure to be a few that you come to like. However, at the same time, there are a few things that really irked me when I played. Chief sin among these was the ending, which I was not very happy about (sorry, it's best to go into these games with literally no idea of what to expect, but it can also be good to manage expectations). It was a game worth your time, but there was definitely room for improvement.
Danganronpa 2, on the other hand, makes me want to give you a solid gold yes. It still has some flaws, but the story is much better, and (unlike DR1) there was hardly a character that I didn't come to like in some way. The visuals were different, but nice. It's my favorite of all the games (though to be fair, there's only 3 + 1, and I've only played through the prologue and chapter 1 of DR3). Again, DR1 isn't terrible, but there are definitely aspects I didn't care for... playing it for DR2, however, makes the whole package more worth it.
As others have mentioned, the humor does get old. They aren't doing theirselves any favors by sticking to memes, 4th wall jokes, and sex humor... it gets kinda old. But DR puts forth some interesting ideas and characters, which is what's really worth sticking around for.
I'd encourage anyone who likes visual novels to pick up DR. The Zero Escape series is good too, but the pacing and inclusion of puzzles make it a very different game, though the story emphasis is very much there. The first game has a pretty fatal gameplay flaw, but maybe they fixed it in the new ports (even if they didn't, the story is still worth putting up with it through the first installment).
TL;DR - Danganronpa should be a pretty solid pick for any visual novel enthusiast, even if it isn't always solid. It's got thoughtful ideas, and will make you think... perhaps a bit more than you thought you would. It can definitely be dark, but it can be really positive, too. I have a ton of screenshots, and I think some of them are pretty darn inspiring.
EDIT: Maybe it's a bit more of an adventure game as well, but consider Life is Strange and Telltale games, too! A nice visual alternative that retains the core idea of story from visual novels, with a bit more interactivity.
