Sleep Inn probably isn't too bad. I typically stay at Comfort Inns, which is owned by the same company, Choice Hotels. I haven't stayed at any of them in that area, but according to their website, there are two other hotels that offer shuttle service to both Fort Lauderdale Airport and Port Everglades.
The hotels are the Comfort Inn Airport / Cruise Port South
and the Comfort Suites Fort Lauderdale Airport West
. I don't know what days you were planning on staying. If you're an AAA member, make sure you specify that when reserving, as this may save you about 10%.
2007 - Majesty of the Seas
2009 - Enchantment of the Seas
2010 - Freedom of the Seas