In fact American tourists are allowed (just recenly though) in Saudi but only under specially organized tours selected by the Saudi government. Similar for Americans that want to visit Iran. Women or course have to wear the hijab/chador but you can now get tourist visas to Saudi.
TWAmerican, as far as Qatar is concerned, they admit to being the Switzerland of the Gulf (although that may be stretching it). They have diplomatic relations with all Arab countries including Iran and Iraq which is more than some of their Arab brethern. They also have a Israel trade mission office in Doha so you could say they have a relationship with Israel which other than Egypt and Jordan, is more than most.
Although booze is legal, it is not as if there are bars around the corner from your hotel. At the Sheraton Doha the bar was hidden from general view, not advertized in the hotel directory, and only foreigners are allowed in. But once in, it had the typical scene, beers, liquor, drunk British expats, Filipino singers etc.
Compared to Dubai, Doha is very very quite. However, the water is beautiful, people are very nice, and with a Ritz Carlton I know believe opened in Doha it is trying desperately to get on the map.
BTW, Casablanca's code is also CAS in addition to CMN. My luggage tags always said CAS on them.