You can walk, run or bike for five miles along the intracoastal on Flagler Drive! Start in the south at Summa Beach Park, a little white-sand cove on the waterway. This is a quiet area with homes and occasional condos. You pass docks all along the way. There is currently construction at Bingham Island Bridge (Jan 2021) that could get in your way, but hopefully that will be over soon.

North of Bingham Bridge, look across the water at the towers of Mar-a-Lago, Trump's mansion.
Just south of George S. Petty Park (halfway along the walk or 2.5 miles in) you go on Washington Rd for a minute, past houses that front the water. But almost the entire walk is directly on the water. 
North of George Petty Park, Flagler Drive becomes more busy with cars so there is quite a bit of noise. There are also plenty of happy people walking along. Here you will find fantastic views of Royal Park Bridge, as well as a public dock near, Valencia Rd, where you can swing your legs above the water. 
North of Royal Park Bridge, you are in the downtown waterfront area of West Palm Beach and there are some enticing cafes like E.R. Bradley's Saloon, with palm trees and water views. There are is a manatee viewing nature area called South Cove Natural area with a long jetty you can walk along, and a large public dock where you can look across at Whitehall, Flagler's mansion.
Once you reach Flagler Memorial Bridge, the five mile walk ends. You could continue along the water for another mile, with more wide-open water views, but this area has higher crime and some homeless people at the beautiful tiled shelters, so the waterfront paths here are not very popular.
There isn't much shade on this walk so do it in winter or in the early morning or early evening.
After your walk, have a coffee at Common Grounds, in the Casa Mara apartment complex. It is so nice in there! The seats are soft so you can stay a while. There are big windows with sunlight coming in. They have great tea in glass teapots, and chocolate croissants. And there are lots of young people from Palm Beach Atlantic University on the weekend. The music is also good. 
For another long and wonderful walk (four miles), on the other side of the intracoastal, on the island, check out the South Lake Trail and continue along the North Lake Trail after. Extend this walk by another half mile, on the south end, by walking along S. Ocean Blvd beside the wave wall, seeing the happy beachgoers and breathing the ocean air. Take the side streets off S. Ocean Blvd to see coconut trees galore (Brazilian Ave, Chilean Ave), and check out the incredible architecture of the little Spanish alleys on ritzy Worth Ave, another side street that is a shopping area. At the end of each of these side streets is S. Lake Dr, where you will see Banyan trees like in Hawaii.
Norton Museum of Art, is just a block west of Flagler Dr. You can walk along Diana Lane, which is a big lawn, to the back of the museum. Ann Norton Sculpture Garden is on Flagler Drive and are also a nice place to visit.

Directions

The five mile waterfront walking path goes from Summa Beach Park in the south to Flagler Memorial Bridge in the north, with a slight detour on Washington Rd for a minute near George Petty Park.
To start at Summa Beach Park, park you car along the street on Seville Rd.
Common Grounds Coffee, in Casa Mara, 3065 S Dixie Hwy, West Palm Beach, FL 33405. Open daily 7am-7pm.

Click on map for interactive view