I have found that LLPSI uses oppidum to describe cities (at least in the early chapters) while Duolingo uses urbe. What is the difference, and which should I usually use?
It is quite common to use urbs to refer specifically to Rome, and the linked dictionary entry even says that oppidum is used for other cities than Rome. You could say that urbs is a capital and oppidum is a regular city. There are a number of ways to phrase and see it, but the crux is: urbs is bigger (in size or importance) than oppidum.
See the links to dictionary entries for more details.
The word urbe is the ablative form of urbs.