I want to really urge you to do coding by hand, if you don't already (looks like the first website is written by hand, though, so I guess this might be unnecessary). WYSIWYG-editors will more often than not leave you with utterly horrible code, and hand-coding will also make finding bugs and fixing irregularities in browsers much easier, since the code will (if written correctly) be more concise, more correct and less bloated. It also basically allows you to think coding while you design, which can make things easier as well, but I guess also limit you in a way.
Also, one of the best tips I've gotten as far as web design goes is the following: Websites are visited by people wanting to read or view content. Obvious, yes, but forgotten so many times by web designers. Presentation of content is the most important thing (aside from, you know, content)! And this means paying attention to margins, paddings, using invisible grids etc. I've seen plenty of beautiful designs/layouts that were basically a white background with text presented in a really tasteful way. Of course, companies, organizations etc. will want things to look good, but it doesn't help if things look good, but actually viewing the content is a bitch. I could probably point you to dozens of websites where the design is really beautiful, but the text is fucking awful to read without highlighting it or changing the size or font or whatever in the browser.
And like Jens said, details can make or break a design. They are important.