There are a few things wrong with this translation, and I checked it with my girlfriend, since I wasn’t too sure about everything either.
Word choice
When I told this sentence to my girlfriend, she asked where Kooshi was. In other words, I don’t think that 港市 is used often. Instead, 町 is the way to denote an arbitrary city.
向かう does not mean to sail, it means to go somewhere, hence without clarification, the sentence could equally well mean that you go there by horse, on foot, or whatever means of travel. Instead, you should say 航海で向かう to mean sailing. (航海 / こうかい = sailing, で = particle, in this case to express the means of doing something)
Grammar
Including 私たちは in the sentence is a common mistake made by people who speak a language in which it is usual to include the subject. In Japanese this is not the case, and actually personal pronouns are usually only included in the sentence as emphasis. In this case, including 私たち will make it sound like you are contrasting “we are sailing to the city” with “they are sailing to the city”; it becomes more like an answer to the question “who are sailing to the city?” than to the question “what are we doing?”
The -て form is very difficult to capture adequately in English, since there is no similar grammatical form in English. The dictionary is right about motion verbs, and something like 行っている can mean both “is still being on the way” and “went and is currently still there”. The thing is, 向かう is not a motion verb, but it expresses a state-of-being, namely the state of being on your way somewhere.
Instead of に you could use まで or へ as well. The difference between に and へ is that に implies that you go to the city for a purpose, while へ means you’re just going there, possibly as an intermediate stop in your travel. まで means until, and has more or less the same meaning as に.
Conclusion
It should be something like 航海で町に向かっている, or politely 航海で町に向かっています