We spent several hours looking around the Katara Cultural Village just outside the city. It’s hard to describe this place, but it was like a free-of-charge entertainment center that included new Qatari-style buildings, a large amphitheater, an arts center, several mosques, a beach, restaurants and a shopping area. I found the architecture in particular fascinating, and also liked a Qatari photo exhibit we visited as well. More about Katara: http://www.katara.net/english/about-katara/about-us/

This is some detail from the mosque at the village, pictured below: