This is a link of many texts, mainly religious. It has both testaments in greek, and many liturgical texts. For example it has the liturgy of st. Chrysostom, which is the most common mass today. Many people know parts of it by heart, because you hear them so often you learn it like a poem.
It has texts in english and modern greek as well.
I thought that those who study NT greek may find it a useful source.
The following link takes you to secular byzantine poetry and texts. I personally love reading them. There are translations to modern greek too. You'll notice the variety of proximity to the ancient style. Some try to sound ancient, some are very close to the modern language.