I've visited Al Zubarah twice. The first time was around 2009/2010 when I was living in Qatar for roughly a year. At that time it was not yet a WHS. Substantial parts of that town were uncovered then and it was really fascinating to see the layout and the different houses. When I returned to Qatar in around 2013/2014 I visited again and found that most of the town was covered up again and there were just a few buildings visible, plus a reconstruction. I can imagine that people are disappointed about this as there really is not a lot to see. On the other hand I can understand why this was done: the town is built from beach rock, just right there from the water edge: tower shells and sand grains cemented together by the high calcium content sea water. Just the few rain showers per year would be enough to dissolve the calcite cement and make the town crumble. My high rating is both based on how I experienced this site the first time, and based on the effort taken on preserving this site. 

Having explored the desert of Qatar extensively I have to say that there are many archaeological sites, including prehistoric rock carvings (they were fenced off in 2013), potentially pre-islamic and pre-Christian graves all across the desert, burial mounts that looks similar to the Dilmun mounts in Bahrain (though in a very poor state), and lots of other things.