I Drive down the day before and have been happy with Comfort Suites on US 1. 2 miles to park N Go and another mile to the cruise terminal. Reasonable rates and I've always had a good experience.
https://www.google.com/maps/dir/Comfort+Suites+Fort+Lauderdale+Airport+%26+Cruise+Port,+302+N+Federal+Hwy,+Dania+Beach,+FL+33004/Port+Everglades+Cruise+Terminal+25,+Eller+Drive,+Hollywood,+FL/@26.0723425,-80.1394441,15z/data=!3m2!4b1!5s0x88d9000c2074b479:0x54dda076e6b3a4d!4m14!4m13!1m5!1m1!1s0x88d9aa5fe2f32fc9:0xd500aa3ac3454cd7!2m2!1d-80.1435727!2d26.0577947!1m5!1m1!1s0x88d901df7e5d96e1:0x7624ceefa59e65ff!2m2!1d-80.1148656!2d26.086819!3e0?authuser=0&entry=ttu