In the last section each pixel is 1,000,000km, and the first section each pixel represents 1 meter, but experience wise it doesn't make the last section feel that much bigger, and I still have to keep looking at the numbers on the bottom to actually perceive the correct scale.
that page lets you appreciate the vast emptiness within which we live..
this link gives some extra details until the page is up http://gizmodo.com/this-scale-model-of-the-solar-system-will...
plus some great links in the comments.
At the 1:10^9 scale, it fits well within a farm or a big park, all the planets are at a viable size, and the Sun is not too big.
The Sun would be 1.5 meters across, the Earth would be 1.2 centimeters across, and the whole thing would be 4.5 km from the Sun to Pluto.
EDIT: Wait! I think this is exactly the scale you're proposing: http://www.jeffreybennett.com/model-solar-systems/voyage-sca...
EDIT2: Well, actually 10^10, so another order of magnitude smaller than 10^9.