So, this guy in town (who owns several prosperous companies) wants me to completely design and implement one of his web sites in my spare time.

What should I charge him for this work (American dollars)?

<span style="color: lightblue">That depends. How big is the web site? What kind of cross-browser compatibility does he want?
If it's a bigger site, obviously charge more. If you need to fill up your nicely designed CSS with hacks to make it look decent in IE (which, as you likely know, neither supports the standards very well, nor gracefully degrades), charge more.

Also, how much of an idea has he given you as to what he wants? That is, how much will you need to design yourself? If he has told you he wants "a web site", you should charge more than if he has told you he wants "these colours, this picture, and this kind of navigation".

You say he owns several prosperous companies. Knowing this, the best ballpark figure I can give you (aside from the above) is high enough that it is plently for you, but low enough that he will not think it an unfair cost.

Why did he approach you in the first place? It doesn't sound like you do this for a living. I think if you set an hourly rate for yourself, $30-40 would be very reasonable and you're probably looking at 15-20 hours anyway, if you're fairly well verst in that sort of thing.

Friend of a friend sort of thing -- he wants me to take a full time position as head of IT / operator, eventually, but I'm putting that off and sticking with occasional contracting for now.

I've worked as a UNIX sysadmin and have all the cool acronyms needed, but I thought some basic web design would be easy money while I was at it.

So, lump sum: 800 - 1000 USD for the job?

Sure, if that is enough for you. The guy sounds fairly loaded, you may aswell get your moneys worth :D

I would do it as an hourly rate, perhaps with an initial review so you have a common understanding of what the scope will be. If you flat-rate bid it, then you need to be wary of that nasty thing called scope creep... that natural occurence characterized by the sounds of "oh, and one more thing..." and "Do you think we could add..."

It's very real and nasty...

You might consider a mix of fixed bid and hourly. Just make sure that you define when you'll be "done" with the initial job, or it may never be over.