We stayed in the Comfort Suites on US 1. It wasn't too bad and it was cheap! When we were there they were doing renovations so if can get a room on a higher floor that would probably be good. We currently live in Ft. Lauderdale and I can check it out for you.
Unfortunately there isn't too much RIGHT THERE, but Las Olas is a few miles down US 1. It would probably be a $10-15 taxi to Las Olas and then you could get dinner and walk the shops and if you walk down Las Olas towards the beach about 3/4 to a mile there are the beautiful homes and all the isles.
There is a hotel that is near my apartment downtown, maybe a courtyard or ramada, I'll check on my way home. That would be within walking to Las Olas restaurants and shops but farther from the port.
On Las Olas is the Riverside Hotel, I think they might be a little pricery. Otherwise you might want to look at the beach, but what you *might* save in hotel you will pay in taxi fares.
There is a Embassy Suites, two double/queens and a pull out double bed/couch. How big is your family? Free happy hour drinks between 5-7 pm. Closer to the port but a bit further from Las Olas and the restaurants. Less than a mile from the Beach. We looked to stay at the Embassy Suites before our cruise in October but it was too pricey then.
The comfort suites would probably be your best bet. It wasn't dirty at all when we were there, just run down but this was October 2005 and they were doing renovations on the top floors and working there way down. It's a $13 taxi from the airport and they have a shuttle to/from the airport and the Port. That's probably your best bet.
I have a spare room, you can stay with me!!

I can see the cruise ships come in and out from my living room/kitchen windows and my balcony!
Edited to add: Check out that Sheraton. It's right at the beach and it looks really nice. Depends on what time you fly in and if you can utilize the beach and stuff. Double check shuttles to and from the port/airport. That's a major hidden cost sometimes!!