FredS, looks like you struck gold with Sknutes - what better sources of information than a female American faculty member who is actually at the AUS!
I've visited Sharjah as well as several of the other emirates, and I've also been to Saudi Arabia many times. At the risk of repeated what previous posters have said,
- the UAE in general tends to be more liberal than Saudi Arabia in many respects, ranging from dress and interaction between the sexes to women's rights.
- Sharjah may be a bit more conservative than the others - as shown by the fact that it is the only "dry" emirate, but this would be far less evident in the academic environment your daughter is considering.
- there is no getting away from the fact that the local population are Islamic, and this fact will be seen in many respects. However, there is a huge foreign population (much of the work is done by foreign workers) and so the locals are used to interacting with foreigners.
- the emirates in general are surprisingly "Western" in many respects, even if much of this "Westerness" is superficial. Your daughter will not lack for KFC or McDonalds, and by the looks of them the shopping centres could just as well be located outside of any American city (with the exception, of course, the way many of the shoppers dress).
- annoyances? as long as your daughter respects the local traditions and mores, there should not be any particular annoyances. Women can walk around without being hassled - as long as they dress accordingly.
- dangers? The UAE is a very safe area. I don't want to get into the politics or human rights issues, but terrorist attacks are just about unheard of in the emirates. There is a huge, repeat huge, difference in this respect among the countries in the Middle East. As for other types of crime, again the UAE is a very safe area, certainly much more safe than American cities! (The major, and this is indeed a major concern, has already been pointed out by Sknutes: traffic can be a horror. Sknutes is being perhaps coy about who are the bad drivers and why, but I would say that too many of the local population get their driver's license too easily, there is too little invested in the policing of traffic, the drivers are very cavalier about wrecking their rather expensive imported cars - and one further danger is the fact that quite a few drivers in Sharjah drive over to another emirate to get drunk, and then get back in their car to drive back. Not good.)
- academic standards? Sknutes can provide you with all types of information on this point, but I can certainly say that the standard of teaching, the standard of the facilities and the overall academic environment in the UAE tend to be world class. The UAE is investing heavily in this sector, and it shows.
I would say that you should give serious consideration to the university at Sharjah. It could be a great opportunity for your daughter to get completely new perspectives on life!