If you want to try something a bit "unordinary", look up Hotel Djúpavík. It's a seasonal hotel, and the owners are wonderful people, very hospitable
http://www.djupavik.com/index.phpThe small town of Vík, on the southern part of the country, is also very nice, and is a great place to "send off" from in west or eastern directions!
Jökulsárlón (the iceberg lagoon) has a small restaurant/cafe that is open during the day(primarily for day tours), and the food is quite tasty. It's a great place to explore, the scenery is (literally) changing, as the changing tides cause the large pieces of ice to shift and move endlessly. I camped there for 2 days, making pictures and just enjoying the serenity of the place as a whole. It really is quite majestic.
Hence why I suggested camping, if you're up for it. It really allows you to experience the country without the boundaries(IMO, aka "comforts") of a hotel room w/ a tv, etc... You're "in it" 24/7