it is my impression that contributors to this course are either hobbyists or probably Arabs living outside and thus the examples given are mostly related to US and Europe (with some few connections to places in the Arab world).
I just hope they develop this course further because so far it is a mix of dialects and standard Arabic, which makes it something like a traveling guide rather than a learning experience.
If you typed (Savannah city ...etc) and was not accepted, then report it (in hope they would fix it, doubt it). Your sentence's translation into Arabic is the same as the above here.
As for the presence and absence of the definite article: Generally speaking, this is one of the issues between Arabic and English when translating from one into the other. This is mainly, I guess, because the concept of the definition article or the idea behind its usage is different in the two languages. Anyway, in the Arabic sentence above, the combination مدينة سافانا is a genitive compound (i.e. X of Y); So, it can be thought of as (city of Savannah). In such compounds, when the definite article is needed, it would be added to the second term in the compound, but sometimes such addition is not possible specially with proper names (like Savanah or one of many other cities' names), so it is left as it is. In English, however, I believe you cannot start with (city of Savannah) but you must state it as either (the city of...) or (Savannah city) right away.
So, the method of using the definite article and the concept behind it is different for each language and on many occasions.
In Genitive relationship (i.e. something belonging to something else), (AL) is only used with the second term. e.g the house of the man becomes بيت الرجل (bayt al-rajul).
This said, in above sentence we have the city of Savannah. The thing here is that Savannah is a proper name and usually does not come with (AL). Hence, there is no (AL) used at all in this combination.