Went to Iceland in May last year. It's a beautiful country, THE most scenic place I have ever visited. My wife and I are in our early 30s, and we like to visit scenic places more so than "happening" places. So, it totally depends on what you like.
Reykjavik has a lot going on, but any other place will be just scenic (and very calm or "boring", if you will).
Iceland is expensive, but less so after the economic crash a few years ago (don't mention it to anyone there though, they don't like talking about it). Hotels can be had for $125-$150. Food is much more expensive. A sandwich lunch for two can be $50.
You can probably drive from Reykjavik to the East end of the country, considering the time you have. We drove to Djupivogur and back. Also went to Olafsvik towards West. We stayed at the Radisson in Reykjavik, and other small hotels elsewhere.
People are incredibly friendly. You will have a great time. You can get miles from Icelandair into your Alaska Airlines account, not AA.