When I had the same issue I bid on a hotel on ft lauderdale beach on Priceline and got a good rate at a nice hotel. Worth a shot. Also check Hotwire hot rates.
We've had good luck with Hyatt Place and I think Hyatt House(??), next to each other, close to FLL and also a shuttle. Free breakfast, nice little bar & food at night. And very cheap, I think $74 last visit.
Another vote for Lauderdale by the Sea. My wife and I always stop for a night or two on the way home from KW. Check out Shore Haven Resort. Not truly a resort but it's clean and affordable, close to everything and only a half hour maybe 40 minute drive to the airport.
We have the same situation and I found reasonable hotels in Hollywood Beach. It's only 20 mins from FLL.
The broadwalk is right on the beach and has lots of hotels, restaurants, and bars on it. We will be able to relax, or get something to eat without having to drive anywhere until we need to leave for the airport.
Another vote for Hollywood beach. Love the boardwalk and plenty to do for a night or two close by if you don't want to drive.
We stay in Pompano Beach. Just a 20 minute drive to airport. Right on beach and many places to choose from.
It appears you are just asking for a place to stay near the airport so I would say the Fairfield Inn & Suites Fort Lauderdale Airport & Cruise Port. Sure, Lauderdale by the Sea is nice so is Hollywood Beach if you want to go out for dinner and drinks and have nightlife, but if you just need something nice, clean, super close to the airport for an early morning flight, this will fit the bill.
We stayed at the Rodeway Inn about 2 miles from FLL last year- it was far from fancy, but was clean and had a pool and restaurant on site (and free breakfast). We used our points, but the regular rates were pretty cheap. We filled up the rental car on the way to the airport and passed a couple of gas stations on the way to do so. It was super easy and quick. We actually ended up getting to the airport really early. There are a bunch of similar hotels as well like other posters suggested. This year we are staying at the new Margaritaville in Hollywood for a couple nights and making a little end of vacation out of it coming back.
There is a Sheraton at Cypress Creek that is very convenient. We stay there when flying out of FLL.