Ozamiz is compact enough that most of the main attractions are within a few kilometres of each other. Tricycles are the standard local transport — they are everywhere, cheap, and will take you anywhere in the city proper for minimal fare. Agree on a price before you get in if the driver does not mention one.
Habal-habal (motorcycle taxis) are also common and useful for reaching slightly more distant barangays. Jeepneys run fixed routes and are the cheapest option if you know where they are headed. For the fort, the cathedral, and the port, you are better off on foot once you reach the waterfront area — the distances are short and the streets around the old town are best seen slowly.
UV Express vans (air-conditioned shared minivans) connect Ozamiz to nearby towns and to Cagayan de Oro. These depart from designated terminals and leave when full, which in a busy city like Ozamiz usually means a short wait.