We usually park right in the parking garage at Port Everglades -- either Northport or Midport, depending on which berth your ship is at. It's a little pricey at $15 a day, but very convenient -- walk off the ship and into your car -- on the road by 8:00 if you do express walk-off.
Otherwise, the Park'n Go on Eller drive is excellent. It's right at the entrance to the port as you come off I595 -- they'll shuttle you over there and it's $8 a day if you book on-line or $12 a day if you pay at the lot. You can also drop your bags first and then drive back out there and park so you don't have to drag all your bags with you on the shuttle. The down side is that when you come back from your cruise, the wait for the shuttle can be crowded.