Yep. I travel to Ft. Lauderdale often for work.
There is a new, kind of small Hampton Inn and Suites JUST off the Sawgrass Expressway (but easily reached from the turnpike too) in Tamrac, FL. It's address is on Madison Avenue (so you know which one if you do a search).
Clean, clean, clean, and no smoking allowed. Decent free breakfasts and microwave and mini refrigerator in the room.