At the moment, I wouldn't recommand Syria either due to the appalling events taking place over there.
But it is true that in more peaceful times, this is a good destination to go for Arabic courses... with Egypt as previously mentioned.
However, to have a good grasp of classical Arabic, no need to go as far away as the tricky thing with Arabic is that you learn a language that unfortunately many people are not able to speak
fluently (except for Arabic teachers and people well-versed in the Arabic grammar)
though they understand it very well (language used for news, speeches, in the newspapers, etc).
So it is not at all like going for example to Germany because you are learning German and you need a 'immersion' in the language. You would have such an immersion in Arabic course for foreigners in Arabic countries but you have just the same here in the UK.
There are some course in this institute having branches in different big cities in the UK ( I am not advertising nor recommanding this company particularly. I never attended a course there. I've just heard about it and people who attended courses there seemed happy. I guess that quality of course is mainly down to the quality of the teacher)
maybe they have summer courses? Or you mentionned uni in 2013. So may be your DD has still one year to have her first taste of Arabic?
A big city like Birmingham has also Arabic courses in a language institute
like Brasshouse Language Center (big center which teaches many many languages!). So maybe you could check all the language institutes in your city (we don't know where you are based)
However, I wouldn't omit to go to the local library to see if they have some books with tapes for beginners.