The Port of Miami (Port Miami) is where you can see all of the cruise ships both coming and leaving from Miami. This is also a major shipping hub. Even if you aren't going on a cruise, its a great place to spot the big ships as they prepare for their next journey. The best view of the port is from the MacArthur Causeway, either by car or by foot. Due to security, you won't be able to enter the Port unless you are going on a cruise or have port related business.
One of the best times to go to the port to spot ships is at sunset. You can watch the sunset over the Miami horizon from the MacArthur