When bored at the computer, I would always go read my favourite webcomics. There are lots of them to choose from, and many have good story and/or drawing, so they are worth a shot. I'll list a few of my personal favourites so you can take off from there if they interest you. All of them are safe.
-Misfile: has kind of an "anime-mainstream" starting point, but then develops into quite an enjoyable read in my opinion. The art is good enough, too.
-Better Days and later on Original Life: an anthro comic series that delves into interpersonal relationships while also managing to be quite humorous all the while. Characters are quite believable in my opinion, and there's a whole lot of development in Better Days, while Original Life is a bit more static for fun. Art starts a bit iffy in Better Days, but quickly improves, being quite good throughout the latter part and the second series. Beware the spoilers if starting with Original Life first.
-Stand still. Stay silent: has an ominous title and not less ominous setting later on, but the mood is quite light-hearted despite of it. The art is breathtaking.
-The GaMERCat: if you like your games, this comical strip is something you can't miss!
-Freefall: the crazy adventures of an alien, a robot and a genetically-engineered anthropomorphic dog/wolf, where absurd humour and scientific fact come hand-in-hand. Art is lower than average, but if you know your science, it is a very enjoyable read.
I used to read more, but I forgot XD I hope it helps.