Most people meet Qatar as a connection at Hamad International. It is worth leaving the airport. Doha has two museums of real depth, the Museum of Islamic Art and the National Museum of Qatar, and Souq Waqif, rebuilt in the old style but still where locals buy spices, falcons and fabric.
Beyond the city the country is flat, sandy and quiet. In the south, dunes run down to Khor Al Adaid, an inland sea that meets the Gulf. In the north are mangroves and the ruined pearling town of Al Zubarah. Three or four nights covers it, alone or on the way to Asia or the Indian Ocean.
The caveats: summer is extremely hot and humid, and Qatar is conservative, with alcohol only in licensed hotels and strict rules on public behaviour.