The SR7(441) and Stirling road area is a busy place and not many good places to ride.
I'd suggest starting at the beach.
Downtown Hollywood is a good place to ride, Hollywood Blvd east of Dixie Hwy. You can ride Hollywood Blvd east to Hollywood Beach which has a bike lane on the walk next to the beach. From there you can go south to Sunny Isles and Miami Beach down A1A which is a great ride or Noth to Ft Lauderdale Beach, Deerfild, Etc. All the above have great sites, many resturants along the way and Bike Lanes.
There is a good bikeshop on Stirling just west of I-95 called Bikes and Boards if you need any tune up, parts, etc.