In urbem/oppidum navigamus would be quite correct, yes. You’re also right about “They are sailing us to Rome/the city”. I wouldn’t worry too much about the opposition of oppidum vs. urbs. Urbs can mean Rome, like when Cicero says “I was out ouf town for the past six months”, but it can also be any other important city, such as Alexandria, or Carthago. While oppidum gives a statement about a town’s structures (i.e., it’s got walls. “There are 28 oppida within the area of the Helvetii and 64 vici (villages)”), urbs gives a statement about its importance (i.e. it’s a capital or metropolis; which implies that the speaker knows the settlement in question). Other settlements are municipium, colonia, civitas, depending on the legal status of their inhabitants within the Roman state and what kind of buildings one might expect there. A civitas is likely to have a bishop in christian times, for example. The whole thing is a bit like the english city/town-distinction wich is very unintuitive to non-anglos.
The pure accusative without preposition do indicate direction is either poetic or restricted to the proper names of cities and the words domus, rus (countryside), and maybe urbs You will find that in your grammar. Oppidum navigamus sound like you are sailors and your cargo is literally the city fortifications and buildings.
Here’s an online grammar that should work quite well for you. Look up the Accusative in the section Syntax.
Yeah, take time for the translation.