I don't actually play visual novel too often, the only one I've played were Danganronpa, ddlc and Steins;gate. I've also purchased all 6 volumes of Higurashi no naku koro ni but I am not strong enough to play this after the kyoAni incident, it's gonna take me a bunch of time to play that game.
Danganronpa is absolutely phenomenal, I absolutely recomand playing all 3 visual novel, there is also a spin-off called ultra-despair girl, that greatly improve one of the character although you can pass on that one if you don't have time/money.
You probably already know all there is to know about ddlc so I'll leave it at that, I was actually lucky enough to get an entirely blind playthrough so I really loved it.
I am currently 17 hours into the steins;gate visual novel (haven't watched the anime) and it is absolutely fantastic, it takes a bit of time to get the gear running but it is definitely worth the time.