I don't know of any hotels with free shuttles to either the pier or airport but in FT Lauderdale it is somewhat a moot point because both are so close to the hotels and to each other.
The average cab from airport to hotel is $20. Most hotels have shuttles that cost $5 to $8 to the cruise ship. (I often get on one for free if there is a group going on a bus and they have a spare seat - but it is a little different if you have a lot of luggage and two people).
But in the long run, just budget for transfers and look for a reasonably priced hotel. Your budget should only need to be about $30 to $50 at the most.