I believe there's an Embassy Suite, Best Western, and the Grande Hotel on 17th Street Causeway that should be less expensive than the Hyatt Pier 66 or the Renaissance. They would be in walking distance to the intracoastal where you can pick up the water taxi. Thank you CF for letting us know the taxi fare has gone up, probably for the season
Anyway, the water taxi is the least expensive way to get around. The first ride, take the tour, all the way to the end. You can jump off and maybe enjoy a beverage or snack at either Shooters or Charlie's. Then you can come back down and get off around Bahia Mar, if you'd like to go to the beach for a while or just walk around the marina and look at the yachts. Then you could get off at one of the Las Olas exits. You could window shop and maybe grab a bite at one of the cafes along Las Olas, there are tons of them. In fact, one of the oldest diners in Ft. Lauderdale is on Las Olas (the Floridian Diner). There are tons of "kitchy" shops on Las Olas, too. I think they have a stop on the water taxi that would get you close to the Elbow Room (Where the Boys Are was filmed there). You can definitely ask the captain or assistant. Hugh Taylor Birch State Park is also another place you can visit. We normally went there for picnics.
The bus system is also very good in Ft. Lauderdale, but I don't know which buses go where anymore. The Galleria Mall is on Sunrise Boulevard. The beach is on A1A and there are tons of places to grab a sandwich or have a beverage.
Hopefully, this will give you a starting point