Glo - a lot depends on if you're simply looking for a place to sleep overnight, then go to the ship, or if you prefer to be in the middle of things - go out to eat, stop at a supermarket or liquor store for "provisions", etc.
Hotels near the airport, most of which have free shuttle service from airport to hotel, will generally be less expensive. But there will also be fewer restaurants nearbyn (possibly, nothing within walking distance), and you'll need transportation to the pier. With a few, you might be able to arrange shuttle transport to the pier but I can't think of any offhand who will offer this free of charge.
Hotels IN Fort Lauderdale, such as the Embassy Suites, Hyatt Place, and several others offer shuttle service from the airport and you can arrange shuttle service to the pier. These hotels, depending upon traffic, are around 10-15 minutes from the airport, and the same to Port Everglades.
Contrary to what I've found in the past, the cruise lines are offering pre and post cruise packages that include transfers from airport to hotel, hotel to pier at rates pretty comparable to what you can obtain on your own, or cheaper. I'm referring to hotels such as Embassy Suites. When you're budgeting, remember that Embassy Suites includes free, full breakfast (all you can eat) in the rate (not just a Continental breakfast) and, if you're there late afternoon/evening, complimentary Happy Hour with "nibbles" that can constitute a meal.
