In the eastern part of Willemstad, there’s some scenic, fairly easy trail running along the coast and around the Jan Thiel Salt Pans. Overall, once can do several km here. There are a couple of distinct sections. 
Coastal Trail. GSV

Mambo Beach Coastal Trail: A dirt trail runs for 2 km between Mambo Beach (near the Aquarium) and Doggy Beach Curaçao. Might also be called the Mariposa Hike. The trail is fairly narrow, rolling hills, passing through scrub brush, affording occasional water views. You could run for 1.3 km and then join the Jan Thiel trails. 

Jan Thiel Salt Pan Trails. This is a network of packed dirt and coral stone trails around the Salt Pan lagoons. There are trails right along the water, and some more inland trails.  There are nice water views, and also this is a prime bird watching area. Keep an eye out for flamingos!
 
The best seamless route is the ~4 km Lagun Walk trail along the eastern edge of the lagoon, starting 1.3 km east of Mambo Beach. You can add some of the inland trails on the east side — some are a bit more rugged and hilly. On the eastern side, there are a couple of km of trails.