There are plenty of hotels near the port, all within 2-3 miles. The airport to the port is 2 miles, all very close.
https://www.google.com/maps/place/1850+Eller+Dr,+Fort+Lauderdale,+FL+33316/@26.0797091,-80.1286049,15z/data=!4m15!1m8!3m7!1s0x88d9000acb53aa5b:0xb27ceb98027011f0!2s1850+Eller+Dr,+Fort+Lauderdale,+FL+33316!3b1!8m2!3d26.0816224!4d-80.1205692!16s%2Fg%2F11bw3_l97g!3m5!1s0x88d9000acb53aa5b:0xb27ceb98027011f0!8m2!3d26.0816224!4d-80.1205692!16s%2Fg%2F11bw3_l97g?entry=ttu
Zoom out 1 click to see the airport. We stay a Hyatt Place on S.E. 10th. street, just off 17th. street. Close to lots of places to eat, all walkable, 2-3 blocks.