I think a good website has a combination of many things.
The overall design/look of the website (colour scheme, fonts, etc). The overall design not only effects the image of the site, if used well it can guide customers through the site by using colour coding of links, different areas of the site etc.
Ease of use - can your customers/ website users find what they want quickly and easily. Not too many menus, not overly complicated menus.
Load times - Still important even with broadband. No one wants to wait ages for a site to load.
Also, although not strictly speaking part of the "design" the content itself. Is it interesting, does it give enough information/the right information and is it spelled correctly.