If you had a good telescope, or something passed you within relatively close range, from what I remember from school, you could see stuff. The red shifted light from galaxies moving away faster than the speed of light due to expansion could be seen with a really good telescope. If something passed within normal visible ranges you would see the object and blue to red shifts past you. Exactly what that would like is not really known.

You would see stuff initially, as like the solar system, then local light emitting bodies, grew further away from you, but you would spend most of your time in still blackness once the part of the universe you were in expands away to far for your eyes to pick up on the light. However I am not an astrophysicist, things might be different than I learned.