Translation:The city of Savannah is a coastal city in the state of Georgia.
I think DL is requiring "city of Savannah" and "state of Georgia" in order to make it clear that you understand how the grammar works in Arabic.
Savannah city is technically correct English, but I've never heard anyone refer to it as Savannah city. Most cities in American English would sound odd referred to as "fill-in-the-blank city". Los Angeles city, Philadelphia city, Chicago city...all of these sound more normal as the "city of fill-in-the-blank". The notable exception would be New York City, which is often referred to in that way.
Obviously, in the US, we would normally just say Savannah, and all would be clear. But it is common in Arabic to phrase it this way, even if the city is well know. For example, you might hear مدينة القاهرة even though everyone in the Arabic speaking world knows that القاهرة is Cairo.
As for the "missing" ال, the Arabic is correctly phrased, but the "the" is needed in English whereas it is not needed in Arabic. The phrase is definite (requiring the) in English because it is a proper name place.
In Arabic, the construction is Idaafa. You can search for that, and Arabic grammar, and turn up all sorts of information to read further if you want. But basically Idaafa refers to the stringing together of nouns to show possession. If you have 2 or more non-proper (not names) nouns strung together in this way to show possession, and the final one is definite (has ال) then the whole phrase is definite. If the final noun is indefinite (no ال) then the entire phrase is indefinite.
But when you are using proper names they are all definite regardless of whether or not they have the definite articles because they refer to only one specific item. You would not use ال with a person's name (الجودي/المحمود), so you wouldn't use it here for the place name Savannah either. However, some place names in Arabic do include the definite article, such as القاهرة، السودان، الأردن, and these will always be written in the Arabic with the definite article.
Here are some examples of Idaafa possession, and whether or not they are definite:
بيت جودي =Judy's house (definite)
بيت الرجل =the man's house (definite)
بيت رجل =a man's house (indefinite)
بيت ام =a mother's house (indefinite)
بيت امي =my mother's house (definite)
بيت ام جودي =Judy's mother's house (definite)
ناس باريس= people of Paris (definite)
بيوت سافانا =houses of Savannah (definite)
(it was a valid comment dj1313 regarding spelling Savannah in English from the Arabic...it requires insider information that there is a city named Savannah in the state of Georgia. But this sort of spelling substitution is often used in Arabic since they don't have a v, as is using ب in place of p (ببسي=pepsi). Sometimes these transliterations require a bit of detecting work, and they aren't always standard, just like transliterations of Arabic to English vary. I remember a sentence about ديلاوير in my early Arabic lessons. It was written under an outline of the state of Delaware which had been flipped left to right along with the text. Someone had to tell me what it was since the picture and the pronunciation were both off).