Origami! It's always fun and there are a ton of resources/guides/tutorials online. Most projects are usually short and practically all are doable in a day. Plus, many projects are cool to show off. Some are even useful! Here's a favorite of mine (simple, takes a couple minutes):

http://www.ehow.com/how_4563591_origami-bookmark.html

However, don't go overboard with the paper :-)

Try ballroom dance. You may be able to find a social dance or a group lesson. It's a good skill to have, and usually good fun, too.

I would argue that this takes more than a day or two.

Given, but he could at least learn a few basic steps, enough to get around the room. He'll also get the exposure to something new, which is most important (and probably what he's looking for).

Learn to surf. Or snowboard. You won't master either, of course. But standings up on your first wave or learning to link turns on the snow is exhilarating, and the first step towards getting better.

I spent some time the last couple days learning two songs on a penny whistle. Great fun.

I thought this would have had more discussion going on, what with everyone here constantly picking up new topics. Anyone else?

How to cook something: how to make an omelette or how to bake bread.

Or how to fix something: a leaky faucet or toilet.

Juggle, or ride a unicycle.

I also second the recommendation to ballroom dance.

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