The Mall/museum idea is a good one, especially if you haven't visited DC before. If the taxi fare is more than what you want to spend, you could take the Washington Flyer bus to the DC Metro.

I don't know of anything worth doing in IAD itself, other than connecting to the internet and getting some work done. But I'm not an expert on that and be interested to hear others' ideas because I anticipate spending a lot of time in IAD next fall when I'll be working in DC for a few months.

Edit: I forgot about traffic. Not sure how well the Washington Flyer bus to the Metro would work in traffic. Others probably know better.