Flying into FLL to take a Carnival cruise in Miami.

Will be coming in around 8pm and leaving the following morning to go onto the cruise ship.

I basically just need a place to stay for the evening.

Should I get a hotel near FLL and grab a taxi in the morning to the port?

Any cheap < $80 hotel?
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Update:

Just completed my cruise. Some info that may be helpful to future travelers:

FLL to Miami: we took a cab from FLL to Miami Hilton for about $75 + tip. There was a bit of traffic. Ride was about 40 minutes.

Hotel: We checked into Miami Hilton, which is 1.5 miles from Port of Miami. I booked a double queen room for $94 + tax using the 50% off Hilton promotion. Got 945 hilton points as well as 500 united miles. Checked out of hotel at 12:30 the next day pm and took a $11 cab ride to port.

Some highlights for those who like to keep connected to the the net:

Bahamas: When you arrive, you go through a visitor center. Near the bathroom and stage, there is actually free wifi. However, very slow and my iphone 5 couldn’t stay connected. Basically, once the passengers from cruise ships come, it overwhelms the system. I did managed to d/l some emails to iphone. Those w/ laptops seem to have better luck staying connected.

St. Thomas: If you have ATT, there is 4G that’s part of ATT national data plan (as St. Thomas is a US territory) but it’s ridiculously slow. You can freely surf the net/txt w/ your smart phone. There are several shops in the downtown area w/ wifi but you have to eat there. You can take $4/person cab ride each way from port to the city.

Puerto Rico: Fast/reliable internet w/ 4G/LTE that’s covered under ATT national plan.

Grand Turks: This is port built by Carnival. It houses two cruise ships at one time. When you walk from dock to shopping area, there is a wifi signal that is p/w protected. However, as you walk more and enter the beach area/margaritaville /pool, there is free wifi. Speed is 1.2 mbps d/l. When you factor 1000+ people trying to access the net w/ these speeds, it’s terribly slow and unreliable. If you need to check your mail quickly, be among the first to get off the ship and go to beach area to pick up free signal. I got a good 30 minutes of internet before system bogged down and was unusable. It remained unusable by time I left 5 hours later.

Port of Miami to FLL: Debarked from Carnival Glory at 7:30 am after we grabbed our luggage and sat in the 3rd floor auditorium. Grabbed a cab and 35 minute ride to FLL was $71 + tip. Arrived at FLL at 8:30am.