I'm anxious to see what this thread turns up. I'm planning a six-week northern Europe trip next year and Iceland is where we are starting out in about July as well.
Watch their world class hockey team. They are really dirty and mean though. The coach got kicked out of the NHL for punching someone to death (or something like that).
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As you can see, I'm completely ridiculous.
There's quite a few day trips out of Reykjavik, the golden circle is the most common and highly recommended one as it covers Gullfoss(The golden falls), Geysir (where the word Geyser comes from, and Ūingvellur which is the location of the mid Atlantic ridge and the worlds oldest parliament began.
Iceland is famous for its nightlife on the weekends, but that again depends if you like to party or not. Its not for the faint of heart as bars often don't start getting busy until 12-1am and going home around 4-6am is quite typical.
To get you started I'd check out these two websites to give you some ideas of the things you can do, the usual stuff such as museums, restaurants, hotels, etc..
I'd take a trip to the blue lagoon while you are there, natural hot springs are such a treat but that one is really been made into a fancy spa and hotel. The price is a bit high, but its a unique place well worth the price of admission, and especially after a long night.
Here's this years tourism video that people got a kick out of, might get you in the mood.
Made a small video slideshow of my last trip this summer to Gullfoss/Geysir, you can skip about 40 seconds in to see pictures from that quick 4hr trip.