Oranjestad is small enough to walk comfortably. The historic centre, the waterfront, Fort Zoutman, and the main museum district are all within about 15 minutes' walk of each other. In the heat of the day, the streetcar running along L.G. Smith Boulevard is a useful shortcut from the cruise terminal to the far end of the shopping strip.
For destinations outside the city centre, the Arubus public bus system runs frequent, cheap services from Oranjestad's main bus terminal near the harbour. Buses to Palm Beach and Eagle Beach run at least every 15 minutes during the day. Taxis are widely available and use fixed rates based on destination rather than meters — always confirm the price before getting in. Rental cars and scooters are available at the airport and from several agencies in town; the island is small enough that a single day's rental covers most of the highlights.
The harbour is the city's main orientation point. L.G. Smith Boulevard runs along the waterfront and is the main artery; the historic centre extends a few blocks inland from it. Most of what you want to see is within a compact area that rewards exploration on foot.