At the time the web was only a couple of years old and it was yet to even hit the "lets get serious" radar of just about everyone.

Essentially, no. There was no one with a very refined aesthetic making websites at the time. Even the Louvre's website (one of the first art museum websites I remember popping up) was extremely ugly.

Drudge Report. Even if you don't like the political "lean" of it (I, personally, don't), you have to appreciate a design that has (basically) stayed the same since it was founded in the mid 90s. The "minimalism" from Drudge had a big impact on a lot of modern web design.

I remember http://www.sgi.com as particularly nice in 96/97. Alas, there aren't many captures on archive.org.

That's the original from 1996 http://www2.warnerbros.com/spacejam/movie/jam.htm

Aww, that's a shame. The old site is a level down: http://www2.warnerbros.com/spacejam/movie/jam.htm