One of the best sites I came across when researching your question was the HubbleSite page. It offers an extensive explanation of the universe, the Hubble Telescope, and images (both live and photographed) from space. It will take you a while to peruse the entire site and read everything (it is a very comprehensive site).
Another site I came across is WorldWide Telescope. This site allows your computer to "function as a telescope." You can explore the universe by examining the Milky Way, planets, and stars.
NASA also offers a site designed especially for students. It is called Imagine the Universe! This site allows students to access satellites and images taken of the universe.
The last site I found by Googling "Turn your computer into a telescope." This site is sponsored by the Griffith Observatory. You can access it at the second link provided below.
I understand your passionate desire to see mysteries of the Universe. There are quite a few simulations out there.
One that is quite popular can be found here:
Its an accurate scale model of our solar system where the Moon is the size of 1 pixel. Just keep scrolling and you'll get a sense of the infinite-- of how much space is just that: space!