All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
There is nothing wrong in opening an Internet café if its owner is able to prevent the users from visiting immoral sites and engaging in unlawful chats. As for hanging images that show a picture of a living thing on the wall of the building or elsewhere in the building, if the picture is that of a woman who reveals what should be concealed of her body, that is absolutely forbidden. But if the picture is free of that, the scholars disagree on its lawfulness. Some scholars regard the picture of a living thing as forbidden, because making images is basically forbidden. Some scholars say that photographic pictures are not forbidden. These scholars looked at the reason for prohibiting pictures, which is rivaling Allah in His Creation. They said that this reason is only found in sculptured and painted pictures. As regards photographing the shadow of a living thing (silhouette), though it is also a creation of Allah, photographing it is not tantamount to rivaling Allah in His creation. Anyway, it is safer and more pious to adhere to the opinion that forbids all kinds of images and pictures, because the textual evidences regarding pictures are general and do not distinguish between types of the pictures of the living thing.
Allah knows best.