Taxi fare from the airport to the port is a set price. $24 I think.
Look at the Hampton Inn Airport South. They have shuttles from the airport, and then from the hotel to the pier. You can book a 'cruise' special and get the shuttle included, or I think they sell a ride for $7 or so.
We always stay at the Holiday Inn, Port of Miami. It is $24 taxi from the airport. It is across the road from the Bayside Marketplace, which is a good place to spend a pre-cruise evening. If you ask you can get a room overlooking the port and see your ship come in. Taxi over to the port was $8 last time we were there, less if a group goes by taxi van.
I think Taxi fares increasing from $25 to $30 from airport to Miami but if you looking for luxury hotels or romantic hotels in Miami with cheap prices then Miami airport motel and Executive Hotel Tropic garden are best choices there. They will provide you executive rooms with every facilities like spa,sauna,gym,pool,garden etc. Hope you enjoyed every moment there with your partner. Best of Luck!!