When you are trying to design a website, it's often useful to look at sites other people have done to get ideas.
Here are a few to look at
Apple Computers
Cool, simple design, lots of white, very nice looking.
Coburn School
Another clean design, lots of white, bright colors, lots of photographs of people. Very nice.
Google
This is a very understated design. Google isn't really trying to dazzle people with amazing graphics. Instead, they focus their energy on making information findable. On that basis, the site is a big success. It's worth taking some time to look at their design to understand how and why it works.
Deviant Art
Collections of art and graphics. You can join and post your own art too.There are websites, and graphics, paintings, textures, and lots of cool other stuff, check it out.
Behance
Similar to Deviant Art, this site allows posting of art of various types. The web design section is interesting if you are looking for examples..
Art Renewal
This is a site dedicated to realism and painting. There is a lot of good art here. It's not really web design but it's still worth a look.
Minimalism in Web Design
Some nice examples of design that isn't cluttered.
Codrops
An article with a collection of interesting website designs.
Futurico
A very nice collection of buttons and design elements.
Sites with terrible design
Los Angeles City College
This website is a train wreck. It's ugly, it's disorganized, and it's very hard to find anything. This website could be improved a lot by choosing a unified design, and by organizing the choices on the front page. Right now there are 58 choices on the front page. If I were designing this I would reduce the number of choices on the front page to: Application, Registration, Administration Services, Departments, Computer Services, Upcoming Events, and Contact Us. All this other stuff should go away. You don't have to put everything on the front page.
Web Pages That Suck
These folks gives annual awards for terrible web design. You can learn as much from looking at the bad ones as from looking at the successes.
I will add more sites later.