"Baghdad is old."
According to A Reference Grammar of Modern Standard Arabic (Karin C. Ryding):
Names of cities are considered feminine because the Arabic word for ‘city’ is madiina, a feminine word. This is true for all cities, not just Arab cities.
It is interesting (but in other languages this "rule" would not be true: in Portuguese, city (a cidade) is a feminine word, most part of city names are feminine, but there are masculine city names).
About country names:
Country names are usually feminine, but there are a few masculine ones, including:
Morocco (...) Jordan (...)
Iraq (...) Sudan (...)
Not sure about the English expression, but the sentence is what it is, simply telling that Baghdad is an old place. I have to admit though that using the adjective قديمة (qadímah) for old here is kind of misplaced. Typically, if I want to describe a historical city I use عتيقة (3atíqah) which also means "old" but let's say it is old with history. Not saying قديمة is totally wrong, but it just doesn't sound right to me as a native as quite mundane in usage to describe a historical place, such as Baghdad (or any other).