I've had good luck at the Holiday Inn at the Port of Miami. It basically right there outside the port entrance and across the street from the Bayside area. So there is a lot to do in walking distance from it. I have never taking a cab from the Hotel to south beach, so I can't answer your second question.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013